In the near-field of a reconfigurable intelligent surface (RIS), the steering vector of the channel between the RIS and a user depends on both azimuth and distance. As a result, new channel estimation schemes, which are required for configuring the RIS and data demodulation, are needed. We study a low-training-overhead parametric maximum-likelihood (ML) scheme that estimates the directional cosine, distance, and complex gain to reconstruct the RIS-to-user channel gain. We derive novel expressions for the Cramér-Rao lower bound for the mean square error (MSE) of the estimated channel parameters and the RIS-to-user channel gain. Using the asymptotic efficiency of the ML estimate, we present novel, insightful expressions for the statistics of the cascaded channel gain between the access point and the user in the presence of errors in configuring the RIS. These are also essential for building its linear minimum MSE estimator. We then derive an expression for the achievable rate in the presence of estimation errors, which leads to insightful, closed-form expressions for the optimal pilot and data powers. Our approach requires fewer pilots than the number of RIS elements and achieves a lower MSE and a higher rate than several benchmarking schemes.

The hybrid medium access control (MAC) protocol, which was first adopted in the IEEE 802.11ax standard, combines contention-based random access (UORA) and contention-free scheduled access (SA) transmissions over orthogonal resource units (RUs). We present a novel fixed-point analysis of saturation throughput and average access delay of hybrid access that accounts for discrete rate adaptation, packet decoding errors, and scheduling. Using this analysis and Markov decision process (MDP) theory, we design a novel dynamic RU allocation policy (ODRAP) for hybrid access. Our analysis and policy design are the first to capture the dynamic flow of users between UORA and SA, and its dependence on the RU allocation. The existing literature has modeled UORA or SA, but not both, or has assumed a fixed number of SA users. We first develop the analysis when the number of packets reported in the buffer status report (BSR) of a user is a geometric random variable. We then present an iterative approach to handle application-specific general distributions. Our numerical results verify the accuracy of the analysis despite its simplicity. Furthermore, they highlight the impact of the number of allocated RUs on the scheduler. ODRAP optimally trades off the throughput with the access delay compared to several benchmark policies.

In over-the-air computation-assisted federated learning (OTA-FL), devices transmit their local models to a parameter server over a shared time-frequency resource. Model aggregation occurs automatically due to the superposition property of the wireless channel. We derive a novel upper bound on the convergence of the optimality gap of OTA-FL that applies to any choice of device transmit powers and receiver scaling. The bound is based on less restrictive assumptions compared to the literature. It leads to the insightful concept of an effective learning rate that captures the dependence of the convergence of OTA-FL on the gains of the channels between the devices and the parameter server. We jointly optimize the transmit powers and the receiver scaling to minimize the error floor implied by the bound while controlling the effective learning rate. This leads to a novel controlled descent algorithm (CDA) and a new variant that adapts the effective learning rate. CDA can be implemented using a low overhead protocol. We benchmark CDA against several transmit power, receiver scaling, and device selection schemes. For both linear regression and multi-class logistic regression, CDA requires fewer iterations and a lower sum energy to achieve a target optimality gap or testing accuracy.

The steering vector for the channel between a reconfigurable intelligent surface (RIS) and a user depends on the distance and the azimuth of the user relative to the RIS when the user lies in the near-field of the RIS. Hence, techniques for estimating the RIS-user channel’s gain differ from those for conventional far-field estimation. This estimate is necessary to configure the RIS phases. We study a low training overhead parametric maximum likelihood scheme that estimates the directional cosine, distance, and complex gain to reconstruct the RIS-user channel. We present a novel linear minimum mean square error (LMMSE) estimator for the access point (AP)-RIS-user effective channel gain. Estimating this channel is necessary to demodulate data. Our estimator is based on novel expressions for the mean and variance of the effective channel gain. It accounts for the impact of errors in estimating the RIS-user channel, which leads to an imperfect RIS phase configuration, and the noise while estimating the effective channel gain. We present novel expressions of the Cramer-Rao lower bound of the mean square error (MSE) of the estimated channel parameters and the RIS-user channel gain. Our approach achieves a lower MSE and a lower symbol error probability than several benchmarking schemes. Fewer pilots than the number of RIS elements are required to achieve a given NMSE.

We propose a novel energy-efficient feedback-enhanced successively reordered transmissions scheme (FE-SRTS) that combines distributed multiple access-based ordered channel access, feedback from the fusion node (FN), and quantized payloads. In FE-SRTS, the sensor nodes sequentially transmit their log-likelihood ratios (LLRs) to the FN until the latter decides. The order in which the nodes transmit is updated based on feedback from the FN and is implemented in a distributed manner using the timer scheme. We derive novel decision rules that enable FE-SRTS to achieve the detection error probability of the optimal rule in which the FN knows the LLRs of all nodes, but with a substantially lower average number of transmissions than conventional ordered and unordered schemes. We also account for retransmissions and power control due to fading, quantized payloads, and feedback. We analyze the average number of sensor transmissions and the total energy consumed by FE-SRTS. The analysis leads to insightful asymptotic results that establish the efficacy of FE-SRTS for Gaussian statistics. Our simulations, based on the Zigbee standard, show that the total energy consumed by FE-SRTS is markedly lower than by conventional schemes.

Full-duplex (FD) communication is a promising new technology that enables simultaneous transmission and reception in wireless local area networks (WLANs). The benefits of FD on the medium access control (MAC) layer throughput in IEEE 802.11 WLANs are well-documented. However, cross-layer interactions between the FD MAC protocol and transport layer protocols such as Transmission Control Protocol (TCP) and User Datagram Protocol (UDP) are less explored. We consider a WLAN with uplink and downlink TCP flows as well as UDP flows between stations (STAs) and a server via an FD access point (AP). We study an STA-initiated FD MAC protocol in which the AP can transmit on the downlink while receiving on the uplink. Using a novel FD-specific STA saturation approximation, Markov renewal theory, and fixed-point analysis, we derive novel expressions for the uplink and downlink TCP and UDP saturation throughputs. Our analysis shows that the AP is no longer a bottleneck and may be unsaturated unlike in conventional half-duplex (HD) WLANs. Despite greater contention and cross-link interference between STAs, FD achieves a higher TCP throughput than HD. FD causes a significant degradation in the UDP throughput. In the unsaturated regime, FD achieves a lower average downlink TCP packet delay than HD.

Beamforming enables millimeter-wave communications to achieve high data rates in 5G and beyond systems. However, accurate beam alignment entails a large training overhead. User device orientation changes and mobility can rapidly lead to beam misalignment and lower the data rate. They also make the beam gains a non-stationary random processes. We propose a comprehensive and novel approach called latent Thompson sampling-based beam selection (LTBS), which combines latent Thompson sampling to track the angle of arrival (AoA) as a latent state, receive beam subset selection based on the sampled AoA in a manner compliant with the 5G new radio standard, rate adaptation, and data beam selection based on predicted throughput. We propose two variants of LTBS that trade-off between complexity and accuracy in modeling millimeter-wave channels. The prior update and channel gain prediction in one of the variants are based on the realistic spatial channel model (SCM). We propose variations that employ windowing to also tackle lateral user mobility, which alters the AoA and the channel statistics. Our numerical results show that the proposed methods track the AoA in a manner robust to user orientation changes and provide higher average data rates compared to conventional and state-of-the-art learning-based beam selection methods.

5G new radio (NR) is based on the mixed-numerology multiple-input multiple-out (MIMO) orthogonal frequency division multiplexing (OFDM) physical layer. Unlike conventional single-numerology systems, subcarriers of different numerologies interfere with each other. The larger Doppler spreads and phase noise that occur at higher speeds and carrier frequencies make the channel vary with time, which affects inter-numerology interference (INI) and exacerbates inter-carrier interference (ICI). We derive novel insightful expressions for the INI and ICI covariances for a mixed-numerology, multi-user MIMO-OFDM system in a wideband spatially correlated time-varying channel with phase noise. On the other hand, the literature has only studied simpler single-input single-out systems or MIMO channels with several limitations. With this analytical foundation, we propose a first-of-its-kind joint INI and ICI mitigation technique that is based on statistical information and incorporates fairness. We derive the precoder for each user that achieves the single-user ergodic capacity. We also determine a novel power allocation that maximizes the weighted sum rate. We solve this using an iterative algorithm based on the difference of convex programming framework. The proposed approach achieves a higher weighted sum rate than several benchmarks. Our results highlight the joint impact of INI and ICI and the influence of various system parameters.

Current generation wireless local area networks (WLANs) based on the IEEE 802.11ax standard employ a novel hybrid medium access control (MAC) protocol, which combines contention-based random access (UORA) and contention-free scheduled access (SA) transmissions over orthogonal resource units (RUs). We present a novel fixed-point analysis of the saturation throughput of IEEE 802.11ax that accounts for hybrid access, discrete rate adaptation, and schedulers. Our analysis captures the dynamic flow of users between UORA and SA in hybrid access. The variability in the number of users, which depends on the number of RUs allocated to UORA and the MAC contention protocol, affects the performance of the scheduler. Our approach differs from the literature, which models either UORA or SA (but not both) or assumes a fixed number of SA users. Our results verify the accuracy of the analysis despite its simplicity and reveal that the conventional approaches can overestimate the UORA and SA throughputs.

The codebook-based scheme for intelligent reflecting surfaces (IRSs) provides flexibility in controlling the training overhead. In it, the reflection pattern with the largest received signal strength is selected from a pre-specified codebook and configured at the IRS. We analyze a training scheme that exploits a novel trade-off between the powers allocated for selection pilots, which are used to select the reflection pattern, and the demodulation pilot, which is used to estimate the channel for demodulation. We develop a novel selection-aware estimator of the beamforming gain of the selected reflection pattern. We derive a tight bound for the achievable rate and an elegant closed-form expression for the beamforming gain. These account for the impact of imperfect channel estimates on the selection of the reflection pattern and the coherent demodulation of the data symbols. The proposed scheme achieves a higher rate than conventional schemes by allocating substantially different powers to the selection and demodulation pilots and data symbols.

In a reconfigurable intelligent surface (RIS)-aided downlink, channel estimation errors due to noise during training lead to a sub-optimal RIS phase-shift configuration. This degrades the RIS beamforming gain. Furthermore, the errors lead to an imperfect estimate of the degraded beamforming gain itself. We analyze the cumulative impact of these errors on the achievable rate. We present two innovations that make our analysis tractable and insightful. First, we present a novel approximation for the effective downlink channel gain in the presence of estimation errors. Second, we prove that the central limit theorem applies to the effective downlink channel gain even in the presence of estimation errors and correlated cascaded channels due to closely-spaced RIS elements. Our analysis leads to insightful closed-form expressions for the optimal pilot and data powers that maximize the rate. The optimal power allocation achieves a significantly higher rate than the conventional approach that assigns equal power to pilots and data.

Full-duplex (FD) communication promises to double the throughput of wireless local area networks (WLANs) by allowing simultaneous transmission and reception of data. While the benefits of FD on the medium access control (MAC) layer throughput of IEEE 802.11 WLANs are well-studied, the interaction between the transmission control protocol (TCP) and the FD MAC layer is less explored. We consider TCP file uploads and downloads between stations (STAs) and a server via an FD access point (AP). Using a novel FD-specific saturation approximation, Markov renewal theory, and fixed point analysis, we derive novel expressions for the TCP upload and download saturation throughputs. These expressions differ from those derived in the literature for TCP over half-duplex (HD) WLANs, and bring out how the AP is no longer a bottleneck. Despite greater contention between STAs, cross-link interference between transmitting and receiving STAs, and asymmetric payloads due to the different sizes of TCP data packets and TCP acknowledgments, we find that an FD WLAN achieves a significantly higher TCP throughput than a conventional HD WLAN.

The codebook-based scheme for intelligent reflecting surfaces (IRSs) decouples the training and control signaling overheads from the number of IRS elements by selecting the IRS reflection pattern from a pre-specified codebook. We analyze the performance of a training scheme that exploits a novel trade-off between the powers allocated for selection pilots, which are used to select the reflection pattern, and the demodulation pilot, which is used for estimating the channel for demodulation. We develop a selection-aware linear minimum mean-square error estimator of the effective channel gain of the selected reflection pattern. When the direct link is blocked, we derive an elegant closed-form expression for the beamforming gain. When the direct link is present, which requires a different analysis, we derive a novel upper bound and insightful asymptotic expressions for the beamforming gain. We then present a novel expression for the achievable rate that accounts for the impact of noisy channel estimates on both selection of the reflection pattern and demodulation of data. We optimize the pilot and data powers and the codebook size. Our approach yields a significantly better rate than conventional schemes, and establishes the advantages of allocating substantially different powers to the selection and demodulation pilots and data.

A fundamental trade-off exists between the time and energy allocated to pilots and data, accuracy of channel estimates, and data rate in a reconfigurable intelligent surface (RIS)-aided system. We optimize the above trade-off for a two-phase training scheme. In the first phase, the base station (BS) estimates the channel from the uplink pilots and configures the RIS. In the second phase, the user equipment estimates the channel from the downlink pilots and coherently demodulates the data. We derive an expression for the achievable rate that accounts for the impact of the channel estimation errors on the RIS phase-shift configuration and data demodulation. Our analysis uses a novel tractable approximation for the effective downlink channel gain and a novel proof that it is asymptotically Gaussian even in the presence of spatial correlation. Our analysis applies to the scenario where enough pilots are sent to estimate the cascaded channels and the cascaded channel grouping scenario that uses fewer pilots. We also study two channel models that depend on the location of the RIS relative to the BS. We derive insightful, closed-form expressions for the optimal powers and training durations. The optimal solution highlights the importance of boosting the pilot powers.

Power-domain non-orthogonal multiple access (NOMA) superimposes signals of multiple users and transmits them simultaneously. To be implemented in 5G and beyond orthogonal frequency division multiplexing systems, it must adhere to the constraint imposed by the standard that the same modulation and coding scheme (MCS) and power must be used across all physical resource blocks (PRBs) assigned to each user. However, the PRBs have different gains in wideband channels and the MCSs must belong to a discrete, pre-specified set. We propose a method that uses the exponential effective signal-to-noise ratio mapping (EESM) to systematically determine whether a feasible power allocation exists for a given choice of MCSs, and to find the MCSs that maximize the weighted sum rate for multiple user NOMA. We then propose a novel power-normalized EESM with backtracking (PB) method. It develops and exploits explicit analytical criteria to check for feasibility. We prove that it is a relaxation of the original problem under various conditions and is exact for narrowband channels. The average weighted sum rate of PB is indistinguishable from that of the EESM-used method despite its lower complexity. It is higher than that of wideband orthogonal multiple access, which is currently employed by 5G.

We propose a novel energy-efficient controlled descent algorithm (EECDA) for over-the-air computation-assisted federated learning. In EECDA, the computing devices transmit their local parameters to the parameter server using amplitude modulation over a common time-frequency resource. As a result, a computation that involves adding the data of multiple users occurs automatically over the wireless channel since the signals superimpose. EECDA adapts the transmit powers of the devices and the amplification at the receiver to minimize the error floor on the optimality gap, which measures the performance of the federated learning algorithm. We derive the transmit powers and receiver amplification in closed-form. This is based on a novel recursive upper bound on the optimality gap that characterizes how wireless channel fades, device transmit powers, receiver amplification, noise variance, and batch selection variance determine the effective learning rate and error floor. For a small total energy, EECDA achieves a markedly lower optimality gap than the conventional minimum mean square error scheme.

Non-orthogonal multiple access (NOMA) superimposes signals of multiple users and transmits them simultaneously. To be implementable in 5G and beyond cellular systems, it must adhere to the constraint imposed by the standard that the same modulation and coding scheme (MCS) and power must be used across all physical resource blocks (PRBs) assigned to the users. However, the channel gains of different PRBs are different in wideband channels and the MCSs must belong to a discrete, pre-specified set. We propose a method that uses the exponential effective signal-to-noise ratio mapping (EESM) to systematically determine whether a feasible power allocation exists for a given choice of MCSs, and to find the MCSs that maximize the weighted sum rate. We then propose a novel, lower complexity method called power-normalized EESM, which leads to explicit analytical criteria for the existence of a feasible power allocation. We prove that this method is a relaxation of the original problem under various conditions and is exact for narrowband channels. Wideband NOMA achieves a higher average weighted sum rate than orthogonal multiple access, which is employed by 5G.

Multi-connectivity enables a 5G cellular system to meet the challenging reliability requirements of downlink ultra-reliable low-latency communication (URLLC) data traffic. In it, multiple base stations (BSs) transmit to the URLLC user by pre-empting time-frequency resources assigned to enhanced mobile broadband (eMBB) users. We derive insightful expressions for achievability, which is the probability that the URLLC user’s block error rate (BLER) requirement is met by multi-connectivity. We do so for both joint transmission (JT) and orthogonal transmission (OT) modes of URLLC for the general case in which the transmissions occur over frequency-selective channels. We then propose a low-complexity algorithm to jointly select the set of cooperating BSs and their modulation and coding schemes (MCSs) to minimize the eMBB throughput loss. For time-varying channels with feedback delays, we present an alternate stochastic reliability requirement for URLLC traffic. The MCS selected on the basis of this requirement has a markedly higher probability of meeting the BLER target over the grid of URLLC user locations. Our results highlight the different trade-offs between URLLC achievability, eMBB throughput loss, and channel state information feedback overhead of OT and JT. They bring out the significant impact of feedback delays even at moderate Doppler spreads.

Mixed numerology has been adopted in the orthogonal frequency division multiplexing-based physical layer of 5G new radio (NR) to serve diverse use cases and services. Since the subcarriers of different numerologies have different bandwidths and symbol durations, they interfere with each other despite being centered at different frequencies. We analyze the inter-numerology interference (INI) encountered by these systems in wideband time-varying channels in the presence of phase noise. We derive novel expressions for the fading-averaged INI power at each subcarrier as a function of the channel’s power delay profile. These lead to insightful, tight bounds for the bandwidth-averaged INI power, which bring out the combined impact of Doppler spread and phase noise. Our comprehensive approach applies to the entire family of numerologies of 5G NR, and accounts for partial subcarrier loading, guard bands, and non-line-of-sight and line-of-sight channels. Our results show that INI affects high-rate modulation and coding schemes (MCSs). To mitigate its impact, we propose a novel statistical square root power allocation scheme that exploits the variation in the average INI powers across the subcarriers. It achieves a lower block error rate than uniform power allocation, which is used in 5G NR.

Multi-connectivity, in which multiple base stations (BSs) cooperate and jointly transmit to a user, enables a 5G cellular system to meet the challenging reliability requirements of downlink ultra-reliable and low-latency communications (URLLC) traffic. We derive insightful expressions for the achievability, which is the probability that the URLLC user’s reliability requirement is met by multi-connectivity. We then propose a low-complexity algorithm to jointly select the set of cooperating BSs and modulation and coding scheme (MCS) to minimize the throughput loss incurred by enhanced mobile broadband (eMBB) users whose time-frequency resources are punctured to carry URLLC data. For time-varying channels with feedback delays, we present a new stochastic reliability requirement for URLLC traffic. The MCS selected on the basis of this requirement markedly increases the probability of meeting the block error rate (BLER) target over the grid of URLLC user locations.

Mixed numerology is a new feature of the orthogonal frequency division multiplexing-based physical layer of 5G new radio (NR). It enables 5G to serve diverse use cases and services. However, the subcarriers of different numerologies, despite being non-overlapping in frequency, interfere with each other due to their different bandwidths and symbol durations. We derive novel expressions for the fading-averaged INI power at each subcarrier of a numerology in a wideband time-varying channel. These expressions cover the general family of numerologies of 5G NR, account for the guard band (which is used to mitigate INI), and apply to line-of-sight (LoS) and non-LoS channels. These lead to insightful expressions and tight bounds for the bandwidth-averaged INI power. They reveal that the INI power increases quadratically with the Doppler spread of the channel and affects higher-rate modulation and coding schemes.

Underlay spectrum sharing addresses spectrum scarcity but imposes constraints on the interference the secondary system causes to the primary receiver. For a secondary transmitter that is subject to the stochastic and general interference-outage constraint and the peak transmit power constraint, we present a novel joint antenna selection and power adaptation rule. It addresses the twin goals of improving the spectral efficiency and reducing the power consumed of an underlay secondary system with low hardware complexity and cost. We prove that the rule maximizes the energy-efficiency (EE) of the secondary system. Its form differs from all other rules considered in the literature. We then present an insightful geometrical characterization of the optimal power of the selected antenna in terms of the channel gains within the secondary system and between the secondary and primary systems. Our approach leads to several special cases, which are themselves novel, and novel analytical insights about the performance and structure of the optimal rule. We also present an iterative subgradient-based algorithm and a simpler non-iterative bound-based algorithm to compute the rule’s parameters. The rule achieves a markedly higher EE compared to conventional approaches, and serves as a new fundamental benchmark for antenna selection in underlay spectrum sharing.

A key problem in underlay device-to-device (D2D) systems is assigning cellular users and D2D users to subchannels to improve spatial reuse while controlling the interference they cause to each other. We present a unified treatment of this problem for two practically motivated partial and statistical channel state information (CSI) models with quantized feedback. They differ in the CSI available at the D2D receiver. In both models, the nodes only have statistical information of inter-D2D and inter-cell interferences, and employ fractional power control. We present two polynomial-time algorithms to assign multiple D2D pairs to subchannels, namely, relaxation-pruning algorithm (RPA) and cardinality-constrained subchannel assignment algorithm (CCSAA). RPA and CCSAA guarantee a D2D sum rate that is at least one-half and one-third, respectively, of the optimal sum rate. We also propose a novel statistical rate upgradation technique that exploits the allocation information to improve the D2D rates. We observe that inter-D2D interference has a more pronounced effect in the statistical CSI model. The algorithms respond differently to the two CSI models. RPA outperforms CCSAA in the partial CSI model, while CCSAA outperforms RPA in the statistical CSI model despite its weaker performance guarantee.

Edge computing with network slicing enables 5G networks to meet the diverse and stringent requirements of new services and applications. We study the problem of admitting network slice requests and serving currently active slices in the 5G edge network, while avoiding active slice redistributions in the network. We pose it as a constrained optimization problem that seeks to maximize the total reward or revenue to the network operator from serving the new and active slices minus a term that penalizes slice redistributions in the network. We propose a three-phase polynomial-time, greedy, heuristic approach called RESET to solve this NP-hard problem. The first phase employs a cost function that determines the order in which new slice requests and a fraction of the active slices are served. It takes into account the bandwidth, storage, and computing requirements of a slice request. The second phase selects an edge cloud (EC) to assign an admitted request based on the residual bandwidth of its incoming links, and storage and computing resources at the EC. The last phase determines the forwarding path to route the traffic associated with the slice request to the selected EC. Extensive simulation results show that RESET achieves a total reward that is competitive with the optimal solution and is higher than benchmark schemes, while requiring far fewer slice redistributions.

For the binary hypothesis testing problem, we propose a novel feedback-enhanced successively reordered transmissions scheme (FE-SRTS), in which the nodes change the order in which they transmit based on the feedback from the fusion node (FN) in each step. It can be implemented in a distributed manner using the timer scheme without any node knowing the measurement of any other node. We derive novel decision rules for it that enable the FN to decide on a hypothesis after receiving only a subset of measurements. For the Bayesian detection framework, FE-SRTS achieves the same optimal error probability as the unordered transmissions scheme (UTS), in which all the nodes transmit their log-likelihood ratios to the FN. However, it requires far fewer nodes to transmit, on average, than UTS, which leads to a much higher energy-efficiency. As the signal-to-noise ratio increases, the average number of transmissions of FE-SRTS decreases to two. This is much lower than the average number of transmissions of the conventional ordered transmissions scheme, which does not employ feedback and does not update the order in which the nodes transmit.

Device-to-device (D2D) communication enables novel proximity services based applications in 5G networks. In underlay D2D, cellular users share subchannels with D2D users leading to interference between them. To efficiently manage the interference and assign D2D pairs to subchannels, we propose a novel relaxation-pruning algorithm (RPA). It allocates at most K D2D pairs per subchannel, where K is a system parameter that controls the trade-off between spatial reuse and inter-D2D interference. RPA is designed for a low signaling overhead scenario. In it, a D2D user feeds back a quantized rate to the base station that meets an outage probability constraint even though the user has only statistical knowledge of the inter-D2D and inter-cell interferences. RPA has polynomial-time complexity. It provably guarantees a D2D sum rate that is at least half of the optimal value, achieving which requires exponential complexity. This is unlike conventional approaches that offer no such performance guarantees or a weaker guarantee. Numerical results show that the D2D sum throughput of RPA is better than conventional algorithms and is within 1% of the optimal value.

We propose a novel joint antenna selection and power adaptation rule that maximizes the energy-efficiency (EE) of an underlay spectrum sharing system. In an underlay system, a secondary user shares the spectrum with a higher priority primary user, but is subject to tight constraints on the interference it generates. Our approach exploits the spatial diversity benefits of multiple antennas to improve the secondary user’s performance, but with a hardware complexity and cost comparable to a single antenna system. We prove that the proposed rule is EE-optimal for a secondary transmitter that is subject to the interference-outage constraint, which generalizes the widely used peak interference constraint, and the peak transmit power constraint. It has a novel form different from the conventional rules considered in the literature. We present an insightful geometrical characterization that brings out the dependence of the optimal power on the channel gains within the secondary system and between the secondary and primary systems. The proposed rule achieves a markedly higher EE compared to conventional rules.

The ordered transmissions scheme requires fewer sensor nodes to transmit their measurements than the conventional unordered transmissions scheme (UTS) in which all nodes transmit. Yet, it achieves the same error probability as UTS. For the practically relevant scenario in which the measurements of the sensor nodes are spatially correlated, we present a novel correlation-aware ordered transmissions scheme (CA-OTS) for the binary hypothesis testing problem with Gaussian statistics. It uses the timer scheme to make the nodes transmit their measurements in the decreasing order of the absolute values of the measurements without any node knowing the measurements of other nodes. CA-OTS applies to the general case where the hypotheses differ in the mean vector and covariance matrix, and markedly reduces the number of transmissions. It differs from the literature that assumes that the measurements of the nodes, when conditioned on the hypotheses, are statistically independent or the covariance matrix has a special structure. When the mean vector or covariance matrix is the same for the two hypotheses, we propose novel refinements that require even fewer transmissions. We also derive insightful upper bounds for them that apply to a general product-correlation model.

In underlay spectrum sharing, transmit antenna selection (TAS) improves the performance of a secondary system and helps it control the interference it causes to a primary system. TAS does so with a hardware complexity and cost comparable to a single antenna system. We present a novel and optimal joint TAS and continuous power adaptation rule for a practically relevant, less explored model in which the secondary transmitter knows only the statistics of channel gains from itself to one or more primary receivers. The rule minimizes the average symbol error probability (SEP) of the secondary system for an entire class of stochastic interference constraints. This general class subsumes the average interference constraint and its novel generalization, and the interference-outage constraint. We derive closed-form expressions for the transmit power and selected antenna. We then develop a general analysis of the optimal average SEP that applies to several widely-used fading models. We also present computationally-efficient approaches to determine the parameters that specify the optimal rule. Our comprehensive numerical results characterize the very different impacts of the interference constraint on both secondary and primary systems. They show that the optimal rule reduces the average SEP by two orders of magnitude compared to conventional approaches.

The use of many narrow beams to overcome the adverse propagation conditions in millimeter-wave channels leads to large training durations and overheads in 5G systems. This causes the beam measurements to become outdated by different extents at the time the transmit and receive beams are selected. The rapid changes in user device orientation exacerbate this problem. We first present a novel modified bivariate Nakagami-$m$(MBN) model to tractably and accurately characterize the joint, non-stationary statistics of the channel gains seen at the times of measurement and data transmission. We then derive a novel and optimal beam selection rule that maximizes the average rate of the system. We use the MBN model to propose a near-optimal, practically amenable bound-based selection (PABS) rule. Our approach captures several pertinent aspects about the spatial channel model and 5G, such as transmission of periodic bursts of reference signals, feedback from the user to enable the base station to select its transmit beam, and the faster pace of updating the data rate compared to the transmit-receive beam pair. The PABS rule markedly outperforms the widely used conventional power-based selection rule and is less sensitive to user orientation changes.

Determining which users to simultaneously schedule on the uplink and the downlink in a full-duplex (FD) system is crucial to control the inter-user interference between them and achieve a high spectral efficiency. The user-pair scheduling algorithm and the efficacy of FD is, thus, closely linked to the availability of channel state information and the feedback scheme that conveys it to the base station (BS). We consider a reduced feedback scheme in which a user that is scheduled feeds back only a limited number of quantized inter-user interferences that are below a pre-specified threshold. For it, we propose a novel user-pair scheduling and mode selection algorithm (UPSMA). We analyze the uplink and downlink spectral efficiencies of UPSMA for two channel models that highlight the different influences of small-scale fading and large-scale shadowing. We derive insightful asymptotic scaling laws that quantify the dependence of the threshold and the uplink and downlink spectral efficiencies on the number of users. UPSMA with limited feedback achieves a higher sum spectral efficiency than a half-duplex system and conventional FD resource allocation algorithms. Its performance is close to the exhaustive search algorithm in which the BS knows all the inter-user interferences.

Differential channel quality indicator (CQI) and wideband CQI are key components of the reduced feedback schemes employed in the 5G New Radio (NR) and 4G Long Term Evolution (LTE) standards. They enable a base station (BS) to acquire channel state information that is essential for rate adaptation and frequency-domain scheduling without overwhelming the uplink. We present a novel throughput-optimal rate adaptation rule that exploits the correlation between the differential and wideband CQIs to improve throughput without any additional feedback. It also shows that the prevalent conventional method that adds the two CQIs is sub-optimal. We then propose a novel flexible-overhead differential CQI feedback scheme, in which the number of bits for differential CQI can be different across the subbands. This provides a new flexibility to the BS to control the feedback overhead. It differs from the current rigid parameterization, in which a user always feeds back a 2-bit differential CQI for each subband. In various single-user and multi-user deployment scenarios involving small-scale fading, large-scale shadowing, and co-channel interference, the proposed approach achieves nearly the same throughput as the feedback scheme employed in 5G and LTE, but with much less overhead.

In a full-duplex (FD) system, the base station (BS) needs to carefully schedule the uplink and downlink users that transmit simultaneously to control the inter-user interference. The efficacy of scheduling is closely tied to the availability of channel state information and the feedback scheme that conveys it to the BS. We propose a novel user-pair scheduling and mode selection algorithm (UPSMA) and a reduced feedback scheme, in which a user feeds back only a limited number of inter-user interferences that are below a pre-specified threshold. We derive expressions for the uplink and downlink rates of UPSMA in the presence of small-scale fading, large-scale shadowing, and pathloss. These lead to novel scaling laws for the threshold and the uplink and downlink rates. Even with limited feedback, UPSMA achieves a higher sum rate compared to a half-duplex system and conventional FD resource allocation algorithms.

Differential channel quality indicator (CQI) and wideband CQI are key components of the 4G and 5G standards. They enable a base station (BS) to acquire channel state information that is essential for rate adaptation and scheduling without overwhelming the uplink. We present a novel throughput-optimal rate adaptation rule, which exploits the correlation between the differential and wideband CQIs to improve throughput without any additional feedback, and a computationally efficient approach to evaluate it. We then propose a novel flexible-overhead differential CQI feedback scheme, in which the number of feedback bits can be subband-specific. The combination of the two approaches provides a new flexibility to the BS to control the feedback overhead and achieves a throughput comparable to conventional approaches with much less feedback.

Ordered transmissions is an energy-efficient scheme that improves the lifetime of a wireless sensor network (WSN) and yet achieves the same performance as the conventional unordered transmissions scheme (UTS) in which all nodes transmit. We present a novel scheme for the binary hypothesis testing problem that exploits ordered transmissions to reduce the number of transmissions for the general and practically important scenario in which the measurements of the sensor nodes are correlated. It differs from the literature that assumes that, conditioned on the hypotheses, the measurements of different nodes are statistically independent or that the covariance matrix has a special structure. In our scheme, the nodes transmit their measurements in the decreasing order of the magnitudes of the measurements. We present two novel approaches to design the decision rules. These address the presence of crossterms between the measurements of different nodes that now arise in the decision statistic due to correlation and make a distributed implementation challenging. Both our approaches markedly reduce the average number of transmissions compared to UTS and ensure that the error probability remains the same.

For underlay spectrum sharing, transmit antenna selection is a low hardware complexity technique that can help the secondary system overcome the performance limitations imposed by the constraints on the interference it causes to a primary system. However, its efficacy depends on the channel state information (CSI) available to the secondary transmitter. We consider a practically appealing model in which the secondary transmitter has only statistical CSI about the channel gains from itself to the primary receiver and is subject to a general class of stochastic interference constraints. We derive an optimal and novel joint antenna selection and continuous power adaptation rule for it that minimizes the average symbol error probability (SEP) of the secondary system. We show that it has an intuitively appealing separable structure. We then analyze its average SEP. Our numerical results evaluate the impact of the interference constraint on both secondary and primary systems, and show that a judicious choice of the interference constraint and its parameters is needed as its impact on the secondary and primary systems can be very different.

Ordered transmissions reduces the number of nodes that transmit in a wireless sensor network (WSN) and yet achieves the same performance as the conventional unordered transmissions scheme (UTS) in which all nodes transmit. However, it breaks down in energy harvesting (EH) WSNs because of missed transmissions by EH nodes that lack sufficient energy. For the Bayesian detection framework, we propose a novel scheme that addresses this challenge for the general case in which the log-likelihood ratio is bounded and has a continuous distribution function. Given the probability that a node misses its transmission, it reduces the average number of transmissions compared to UTS. For truncated Gaussian statistics, we then propose a novel refinement that requires even fewer transmissions and that simultaneously lowers the error probability. We also analyze its performance and show that it lends itself to a computationally-efficient Monte Carlo evaluation. When the time evolution of the battery energies of the nodes is tracked and the probability of a missed transmission becomes a function of the scheme itself, the proposed schemes achieve a markedly lower error probability than both UTS and sequential detection, except when the energy harvested is so less that very few nodes can transmit.

In underlay spectrum sharing, the interference constraint limits transmissions by the secondary transmitter, which concurrently accesses the spectrum, to protect the primary user from excessive interference. Transmit antenna selection enables a secondary user to overcome the limitations imposed by the interference constraint using low-complexity hardware. We develop an optimal and novel joint antenna selection and power adaptation rule that minimizes the average symbol error probability (SEP) of a secondary user that is subject to two practically well-motivated constraints. The first is the less-studied but general interference-outage constraint, which limits the probability that the interference power at the primary receiver exceeds a threshold. The second constraint limits the peak transmit power of the secondary transmitter. We show that the optimal rule for the interference-outage constraint has a novel structure that is markedly different from the rules considered in the literature. We then present an insightful geometric interpretation of its structure. Using this, we also propose a practically amenable and near-optimal variant of the optimal rule called the linear rule, and analyze its performance. Our numerical results show that the optimal rule reduces the average SEP by one to two orders of magnitude compared to the rules in the literature.

Underlay spectrum sharing improves spectral utilization by allowing a secondary user to transmit concurrently with a primary user. However, the secondary user's performance is limited by the interference constraint that is imposed on it to protect the primary user. Transmit antenna selection overcomes this limitation with a hardware complexity comparable to a single-antenna system. We present a novel and optimal joint antenna selection and power adaptation rule for a secondary system that is subject to the practically motivated interference-outage constraint, which is more general than the widely studied peak interference constraint. The rule provably minimizes the average symbol error probability (SEP) of the secondary user. We show that it has a fundamentally different and novel structure compared to the ones studied in the literature. We present key geometric insights about its novel structure. We use these to propose a simpler, linearized, and near-optimal variant. Compared to the rules considered in the literature, the proposed rules reduce the average SEP by an order of magnitude.

We address the problem of allocating multiple device-to-device (D2D) pairs per subchannel in a multi-cell scenario with multiple subchannels and unknown inter-D2D and inter-cell interference. We propose a scheme to feedback q bits about the signal-to-interference-plus-noise ratio of a D2D pair for each subchannel that ensures that the D2D rates can be achieved with a pre-specified probability of outage. Along with this, the base station (BS) has only statistical information about the inter-cell interference, and has to provide a quality-ofservice guarantee to the scheduled cellular users. We formulate the subchannel allocation problem as a generalized assignment problem, and propose a low-complexity locally greedy algorithm (LGA) to solve it. LGA provably achieves a D2D sum rate that is at least 1/2 and 1/3 of the maximum achievable D2D sum rate for q = 1 and q ≥ 2, respectively. We then propose a rate upgradation (RU) step that enhances the D2D rate by exploiting an inherent asymmetry in the channel state information (CS!) at the BS and D2D pairs. LGA with RU achieves a spectral efficiency that is markedly better than conventional approaches that assign one D2D pair per subchannel, and close to that of a system with full CS! of the intra-cell links even for small q.

Opportunistic transmission schemes improve the lifetime of conventional wireless sensor networks (WSNs) by reducing the number of transmissions. However, this comes at the expense of performance since fewer measurements are available. We show that in energy harvesting (EH) WSNs, in which the sensor nodes harvest energy from the environment, this trade-off is fundamentally different. For a general model in which the nodes experience independent and non-identical fading and the EH process at a node is stationary and ergodic, we present lower bounds on the mean squared error (MSE) for two important classes of channel-based opportunistic transmission schemes, namely, censoring and ordered transmissions. For the latter, we present two novel variants that arise depending on whether the energy in the battery of an EH sensor node is accounted for before ordering or not. For censoring, the lower bound leads to an insightful and explicit characterization of the optimum censoring threshold for each node. For ordered transmissions, it helps determine the optimal number of nodes that should be selected to transmit. We find that the ordered transmission schemes can outperform the censoring scheme. We also propose a hybrid scheme that combines the best features of the above schemes for EH WSNs.

The asymmetric network model, in which the access point (AP) is full-duplex (FD) capable while the other nodes are only half-duplex (HD) capable, is motivated by early-stage deployments of FD-capable networks. We propose a medium access control (MAC) protocol called asymmetric FD MAC (AFD-MAC) for this model. It leverages features such as random back-off and carrier sensing of the widely-used 802.11 HD MAC protocol, and it introduces two signals to exploit the FD capability of the AP. We also develop a general, network topology-specific renewal-theoretic analysis that characterizes the saturation throughput of AFD-MAC. It captures the differences in the statistical properties of the nodes and the AP due to differences in their duplexing capabilities or the number of hidden nodes. AFD-MAC can increase the throughput by a factor as large as two and can reduce head-of-line delay by a factor more than half compared to the conventional 802.11 HD MAC protocol. The gains depend on the ratio of the uplink to downlink packet lengths, network topology, and the extent of self-interference cancellation. A contrarian insight that emerges is that hidden nodes can enable the network to exploit its asymmetric FD capability.

In underlay device-to-device (D2D) communication, assigning more D2D pairs to a subchannel can increase the spectral efficiency but it also increases the inter-D2D interference and causes interference to the cellular users (CUs). We consider the assignment of at most K D2D pairs per subchannel in a multi-cell scenario with multiple uplink subchannels. We propose a q-bit quantized feedback and resource allocation model that provides a quality-of-service guarantee to the CUs and ensures that the rates assigned by the base station (BS) to the D2D pairs can be decoded with a pre-specified outage probability even with unknown intercell and inter-D2D interferences. We propose a novel, polynomialtime, cardinality-constrained subchannel assignment algorithm (CCSAA) that applies for any K and achieves at least 1/2 and 1/3 of the optimal D2D sum throughput for q = 1 and q ≥ 2 bits, respectively. We also propose an alternate cardinality-constrained locally greedy algorithm (CCLGA) that has an even lower complexity and is just as effective in practice. We present a rate upgradation step that exploits the inherent asymmetry in the channel state information at the BS and D2D users to improve spectral efficiency. Our approach also addresses a novel extension to dynamic two-way D2D communications.

Reduced feedback schemes are crucial in achieving the high data rates expected of orthogonal frequency-division multiplexing-based 4G and 5G cellular systems. They ensure that the feedback overhead required for acquiring the channel-state information to enable downlink scheduling and adaptive modulation and coding at the base station (BS) does not overwhelm the uplink. We present a novel modeling and analysis of the single-user and multi-user throughputs of the differential feedback scheme that is used in both 4G and 5G standards. In this feedback scheme, a user feeds back a 4-bit wideband channel quality indicator (CQI), which indicates the rate that the user can decode if the BS was to transmit to it over the entire system bandwidth, and a 2-bit differential CQI for each subband relative to it. Our analysis incorporates co-channel interference, different single-stream multi-antenna modes, and different schedulers, which cover a wide range of the tradeoff between the throughput and user fairness. It brings out several insights such as the increase in the throughput as the correlation between subbands increases and how differential feedback reduces the overhead significantly while only marginally reducing the throughput.

Transmit antenna selection is a low-complexity multiple-antenna technique that exploits spatial diversity using only one radio frequency chain. We investigate it for an underlay cognitive radio system that operates in the presence of multiple primary receivers and is subject to a constraint on the interference outage it causes at any of the primary receivers. The selection is based on a practically motivated and general partial channel state information (CSI) model in which the secondary transmitter (STx) only knows the channel power gains to a subset of the primary receivers. We derive a novel and general antenna selection rule that provably minimizes the symbol error probability (SEP) of the secondary system. We also derive insightful analytical expressions for its average SEP and interference-outage probability. These apply to a general class of channel fading models and any number of transmit and receive antennas, and include the special cases in which the STx knows channel power gains of all or none of the primary receivers. Our numerical results bring out a new insensitivity of the average SEP of the optimal rule to the interference power threshold when the CSI available is partial.

Censoring improves the lifetime of conventional wireless sensor networks (WSNs) by reducing the number of sensor node transmissions. However, this comes at the expense of performance since measurements from fewer nodes are available. We show that in energy harvesting (EH) WSNs, in which the sensor nodes harvest energy from the environment, this trade-off is fundamentally different. For a general model in which the nodes experience independent and non-identical fading and the EH process at a node is stationary and ergodic, we derive a lower bound on the mean squared error (MSE). It leads to an insightful and explicit characterization of the optimum censoring threshold for each node. We show that it is the point at which the probability that an EH node has sufficient energy to transmit becomes 1. We also analyze the MSE outage probability, which is an alternate and widely used performance measure, which characterizes the impact of channel fading.

Reduced feedback schemes play a critical role in contemporary orthogonal frequency division multiplexing systems such as Long Term Evolution (LTE). They ensure that the channel state information required for downlink rate adaptation and scheduling is available at the base station (BS) without overwhelming the uplink with feedback overhead. We present a novel model and analysis of the single-user and multi-user throughput of the widely used differential feedback scheme of LTE, which is called eNodeB-configured subband feedback. In it, a user feeds back a 2-bit differential channel quality indicator (CQI) for each subband relative to a 4-bit wideband CQI, which indicates the rate that the user can decode if the BS were to transmit over the entire system bandwidth. Our analysis applies to many multi-antenna modes. In addition to bringing out several insights, it shows that differential feedback can reduce the feedback overhead significantly while incurring only a marginal reduction in throughput.

We propose a novel energy-efficient ordered transmissions scheme for Bayesian hypothesis testing in energy harvesting (EH) wireless sensor networks (WSNs), in which the EH nodes harvest energy from the environment and can replenish their batteries. The proposed scheme exploits the distributed timer scheme to ensure that the nodes transmit their readings to the fusion node in the decreasing order of their log likelihood ratios without any node knowing the readings of any other node. It addresses the new problem of missing transmissions that arises in EH WSNs because the energy harvested by the nodes is random. We show how the disruption caused in the sequence of ordered transmissions by these missing transmissions can be tackled. The proposed scheme not only reduces the number of transmissions, but also reduces the error probability compared to the conventional unordered scheme in which all the sensor nodes attempt to transmit in a pre-determined order. This is unlike several energy-efficient techniques that reduce the number of transmissions but increase the error probability.

Opportunistic selection is a key technique to improve the performance of wireless systems. In it, one among the available users is selected on the basis of their channel gains or local parameters, such as battery energy state. Formally, each user possesses a real-valued metric that only it knows, and the goal is to select the best user, which has the highest metric. The splitting algorithm is a popular, fast, and scalable algorithm to implement opportunistic selection; it is distributed and guarantees selection of the best user. We show that this algorithm, which has thus far been designed assuming that the metrics are independent and identically distributed, is no longer scalable when the metrics are correlated. We then propose a novel correlation-aware splitting algorithm (CASA) and show how it can be applied to practically motivated probability distributions and correlation models. We present computationally feasible techniques for pre-computing the thresholds that CASA specifies, thereby ensuring that CASA can be implemented in practice. We benchmark the performance of CASA with the conventional algorithm, and show that it reduces the average selection time significantly as the number of users or the correlation among them increases.

Transmit antenna selection (TAS) is a technique that achieves better performance than a single antenna system while using the same number of radio frequency chains. We propose a novel TAS rule called the λ-weighted interference indicator rule (LWIIR). We prove that for the general class of fading models with continuous cumulative distribution functions, LWIIR achieves the lowest average symbol error probability (SEP) among all TAS rules for an underlay cognitive radio system that employs binary power control and is subject to the interferen-ceoutage constraint. This constraint imposes a limit on the probability that the interference power at the primary exceeds a threshold. It is a generalization of the widely studied peak interference constraint. We then derive the average SEP of LWIIR. The insightful performance analysis applies to any number of transmit and receive antennas and to many constellations. We also analyze the practical scenario in which the secondary transmitter has imperfect information of the channel gains from itself to the secondary and primary receivers. We show that the imperfections in these two sets of channel gains have different impacts on the system. Our benchmarking shows that LWIIR outperforms many selection rules considered in the literature.

Device-to-device (D2D) communication enables simultaneous data transmissions by cellular users (CU) and D2D user pairs, but at the expense of additional interference between them. The literature on resource allocation in D2D systems often assumes that the base station (BS) has complete channel state information (CSI) about all the links between all the users in a cell. However, acquiring the CSI of cross links between the CUs and the D2D receivers is a critical bottleneck because the number of cross links is the product of the number of CUs and D2D pairs. We study a novel partial CSI model in which the overhead of feeding back the CSI of the cross links is much lower. For a cell with one D2D pair and multiple CUs, we propose a novel throughput-optimal joint mode selection, user scheduling, and rate adaptation policy that exploits information about the statistics of the cross links and incorporates inter-cell interference. We derive closed-form expressions for the feedback-conditioned goodput for the underlay mode, which drives this optimal policy. We also present extensions that incorporate user fairness, quantized CSI, and multiple D2D pairs and multiple subchannels.

Transmit antenna selection (TAS) is a low hardware complexity multiple antenna technique that exploits spatial diversity to improve the performance of an interference-constrained cognitive radio (CR) system. In the underlay access mode of CR, the choice of the transmit antenna depends on the link between the secondary transmitter (STx) and its receiver, the interference link from the STx to the primary receiver (PRx), and also the interference constraint imposed on the CR system. We propose a novel selection rule called the lambda-weighted interference indicator rule for an underlay CR system that is subject to the interference-outage probability constraint, which constrains the probability that the interference power at the PRx exceeds a threshold. This general constraint also encompasses the widely studied peak interference power constraint. We prove that the proposed rule minimizes the average symbol error probability (SEP) of the CR system. It applies to a general class of fading models with continuous probability distributions and many constellations, and outperforms the many selection rules studied in the literature. We analyze its SEP, and present several insights about its novel structure and behavior.

The availability of channel state information (CSI) about the interference links from the secondary transmitters to the primary receivers is widely assumed in the literature on underlay cognitive radio (CR) in order to control the interference caused to the primary network. However, when multiple primary receivers are present, acquiring such CSI about all the interference links in a timely and scalable manner is practically challenging. We study an underlay cooperative relay system, in which the channel gains of only a subset of the interference links are available at the source and relays. Based on such incomplete CSI, the source and relays back-off their transmit powers in order to satisfy an interference outage constraint. We derive a tight upper bound on the outage probability of the secondary system for the rate-optimal relay selection rule. Our numerical results show the effect of incomplete CSI on the secondary system performance and how its impact can be ameliorated.

Cooperative relaying combined with selection exploits spatial diversity to improve the performance of interference-constrained secondary users in an underlay cognitive radio (CR) network. While a relay improves the signal-to-interference-plus-noise ratio (SINR) of the secondary network, it requires two hops and also generates interference to the primary network. We present a novel, optimal relay selection rule that maximizes the fading-averaged transmission rate of an average interference-constrained underlay secondary network. It differs from the several ad hoc incremental relaying schemes proposed in the literature, while requiring a feedback overhead that is comparable to them. We then analyze the average rate of the optimal rule. We also present insightful high and low SINR asymptotic analyses, which bring out the extent to which the use of the relays improves the average rate as a function of the system parameters. Our numerical results show that the proposed rule outperforms several known relay selection schemes for CR, and also characterize the regimes in which some of these schemes are near-optimal.

In orthogonal frequency division multiplexing systems, reduced feedback schemes provide essential channel state information from the users to the base station (BS) without overwhelming the uplink. For the practically important best-M scheme, in which each user feeds back only its M strongest subchannels and their indices to the BS, we derive a novel, throughput-optimal scheduling and rate adaptation policy that enables the BS to schedule the best user and its data rate for all the subchannels. The policy exploits the structure of the information fed back by the best-M scheme and the correlation among subchannel gains. We present it in closed-form for the widely studied exponential correlation model. Using insights gleaned from the optimal policy, we propose a novel, low-complexity two subchannel reduction approach, which is seen empirically to be near-optimal and easily handles practically important general channel correlation models, quantized feedback, and co-channel interference in multi-cell scenarios. Compared with several ad hoc approaches, the proposed approaches improve the cell throughput without any additional feedback. A modified gradient-based opportunistic scheduler is also proposed to ensure user fairness.

Rate adaptation and scheduling are essential in ensuring that contemporary orthogonal frequency division multiplexing systems achieve high downlink spectral efficiencies. They depend upon reduced feedback schemes to efficiently feedback channel state information from the users to the base station (BS). In the popular threshold-based quantized feedback scheme, a user feeds back to the BS the quantized value of the signal-to-noise ratio for each subchannel. For this scheme, we derive a novel, throughput-optimal discrete rate adaptation (TORA) policy, which enables a system designer to reduce the feedback overhead. We present it in closed form for different multi-antenna diversity modes for the exponentially correlated subchannel gains model. We also develop a computationally simpler suboptimal variant of it. We derive an insightful lower bound for the fadingand user location-averaged throughput gain achieved by TORA over conventional rate adaptation for 1-bit feedback. We present extensive results to benchmark the system-level performance of TORA for different numbers of feedback bits and modulation and coding schemes available at the BS, and various schedulers, quantizers, and multi-antenna modes.

In rate-adaptive orthogonal frequency division multiplexing (OFDM) systems, limited feedback schemes are essential to reduce the number of subchannels for which the channel state information is fed back by the users. For the practically important best-M scheme, in which each user feeds back only its M strongest subchannels and their indices to the base station (BS), we derive a throughput-optimal rate adaptation policy that enables the BS to assign rates to the subchannels of every user. We present it in closed-form for the widely used exponential correlation model. The novelty of the policy lies in its exploitation of the structure of the information fed back by the best-M scheme and the correlation among subchannel gains. We also present a near-optimal, lower computational complexity approach. In effect, our approach facilitates rate adaptation and scheduling by the BS even on subchannels that are not fed back by a user due to feedback constraints. For various schedulers, we show that it improves the downlink throughput compared to several conventional approaches, without requiring any additional feedback.

Time-variations in wireless channels affect opportunistic selection in a multi-node wireless system in two ways. First, the selected node can become sub-optimal by the time data transmission commences. Second, the channel changes during data transmission. We develop a comprehensive and tractable analytical framework that accurately accounts for both these effects. It differs from the extensive existing literature that primarily focuses on time-variations until the data transmission starts. We first develop a novel concept of a time-invariant effective signal-to-noise ratio (TIESNR), which tractably and accurately captures the time-variations during the data transmission phase with partial channel state information available at the receiver. Thereafter, we model the joint distribution of the signal-to-noise ratio at the time of selection and TIESNR during the data transmission and analyze the average packet error rate (PER). Extensive numerical results verify the accuracy of each step of our approach and show that ignoring the correlated time-variations during the data transmission phase can significantly underestimate the average PER.

Radio-frequency (RF) energy harvesting (EH) is an appealing solution for making wireless sensor networks (WSNs) self-reliant in terms of energy. We investigate the problem of sensing and estimation in a WSN for a practically motivated transmit and receive model. In it, noisy readings are communicated by multiple peak-power constrained RF EH sensor nodes in an analog manner using phase modulation to a fusion node, which uses the popular phase-locked loop (PLL) circuit for signal reception. For the time-sharing model, in which an EH sensor node alternately harvests energy and transmits data, and for a general class of stationary and ergodic RF EH processes, we present insightful expressions for the mean squared error (MSE) of the estimate at the fusion node, and optimal fraction of time a node harvests energy and optimal transmit power that minimize the MSE. Benchmarking with several digital schemes brings out the natural adaptability and efficacy of the considered scheme.

Reduced feedback schemes play a critical role in orthogonal frequency division multiplexing-based cellular systems because they facilitate scheduling and rate adaptation by the base station (BS) while reducing the number of subchannels for which channel state information is fed back by the users. We address the problem of reliable transmission even on subchannels that are fed back by a few users due to feedback constraints. For the practically relevant best-M feedback scheme, in which each user reports only its M strongest subchannels to the BS, we derive a nonlinear constrained minimum mean square error estimator that enables the BS to estimate the signal-to-noise-ratios of all the subchannels of every user. We then propose two lower computational complexity approaches that incur a negligible loss in performance. The novelty of these approaches lies in their exploitation of the structure of the best-M feedback information and the correlation among subchannel gains. Applications to general channel models and to quantized feedback are also shown. In terms of system level impact, the proposed approaches improve the cell throughput compared to several conventional approaches - without requiring any additional feedback - for uncorrelated and correlated subchannels, and for various schedulers.

Reduced feedback schemes facilitate scheduling and rate adaptation in orthogonal frequency division multiplexing systems while reducing the number of subchannels (SCs) for which channel state information (CSI) is fed back. In the popular selective feedback scheme, each user feeds back CSI about only its strongest SC to the base station (BS). We focus on the less studied, but practically important problem of transmitting reliably even on SCs that are fed back by no user or few users. We derive a constrained, non-linear minimum mean square error estimator that enables the BS to estimate the power gains of all the unreported SCs of a user. The novelty of the estimator lies in its exploitation of the structure of feedback generated by the selective feedback scheme. It improves the average cell throughput compared to several conventional approaches - without any additional feedback overhead. The improvements occur for both uncorrelated and correlated SCs, and for the channel-aware greedy and fair round-robin schedulers.

Cooperative relaying combined with selection exploits spatial diversity to improve the performance of interference-constrained secondary users in an underlay cognitive radio network. While a relay improves the signal-to-interference- plus-noise ratio, it requires two hops and also generates interference to the primary. Therefore, in underlay cognitive radio, new criteria are needed to determine which relay to select. We present an optimal relay selection rule that maximizes the fading-averaged transmission rate of an average interference-constrained underlay secondary network. It differs from the many rules proposed in the literature. We then analyze its fading-averaged channel capacity. Numerical results show that the proposed rule outperforms direct transmission and several other rules, such as incremental relaying, proposed in the literature.

Cooperative relaying combined with selection exploits spatial diversity to significantly improve the performance of interference-constrained secondary users in an underlay cognitive radio network. We present a novel and optimal relay selection (RS) rule that minimizes the symbol error probability (SEP) of an average interference-constrained underlay secondary system that uses amplify-and-forward relays. A key point that the rule highlights - for the first time - is that, for the average interference constraint, the signal-to-interference-plus-noise-ratio (SINR) of the direct source-to-destination (SD) link affects the choice of the optimal relay. Furthermore, as the SINR increases, the odds that no relay transmits increase. We also propose a simpler, more practical, and near-optimal variant of the optimal rule that requires just one bit of feedback about the state of the SD link to the relays. Compared to the SD-unaware ad hoc RS rules proposed in the literature, the proposed rules markedly reduce the SEP by up to two orders of magnitude.

Managing inter-cell interference is one of the main challenges in current and next generation wireless systems that aggressively reuse the frequency. Cooperation between interfering cells has been sought to mitigate interference. In this paper, we address the problem of jointly optimizing the transmit powers, user scheduling, and user association in a cellular network to maximize the weighted sum rate (WSR). To this end, we develop a distributed interference penalty algorithm in which the cells update their transmit powers and user schedule to maximize its utility minus an interference cost. The proposed algorithm involves only limited exchange of information via backhaul and has convergence guarantees. Furthermore, we propose a sub-optimal algorithm with lower computational and backhaul overhead. In it, the users are first associated to the base stations (BSs) based on their signal-to-interference-plus-noise-ratios (SINRs). It is then followed by joint optimization of BS transmit powers and user scheduling, for which we develop an interference penalty algorithm as well. We show that the proposed algorithms outperform the computationally complex weighted minimum mean squared error (WMMSE) algorithm.

In several wireless sensor networks, it is of interest to determine the maximum of the sensor readings and identify the sensor responsible for it. We propose a novel, decentralized, scalable, energy-efficient, timer-based, one-shot max function computation (TMC) algorithm. In it, the sensor nodes do not transmit their readings in a centrally pre-defined sequence. Instead, the nodes are grouped into clusters, and computation occurs over two contention stages. First, the nodes in each cluster contend with each other using the timer scheme to transmit their reading to their cluster-heads. Thereafter, the cluster-heads use the timer scheme to transmit the highest sensor reading in their cluster to the fusion node. One new challenge is that the use of the timer scheme leads to collisions, which can make the algorithm fail. We optimize the algorithm to minimize the average time required to determine the maximum subject to a constraint on the probability that it fails to find the maximum. TMC significantly lowers average function computation time, average number of transmissions, and average energy consumption compared to approaches proposed in the literature.

Cooperative relaying combined with selection has been extensively studied in the literature to improve the performance of interference-constrained secondary users in underlay cognitive radio (CR). We present a novel symbol error probability (SEP)-optimal amplify-and-forward relay selection rule for an average interference-constrained underlay CR system. A fundamental principle, which is unique to average interference-constrained underlay CR, that the proposed rule brings out is that the choice of the optimal relay is affected not just by the source-to-relay, relay-to-destination, and relay-to-primary receiver links, which are local to the relay, but also by the direct source-to-destination (SD) link, even though it is not local to any relay. We also propose a simpler, practically amenable variant of the optimal rule called the 1-bit rule, which requires just one bit of feedback about the SD link gain to the relays, and incurs a marginal performance loss relative to the optimal rule. We analyze its SEP and develop an insightful asymptotic SEP analysis. The proposed rules markedly outperform several ad hoc SD link-unaware rules proposed in the literature. They also generalize the interference-unconstrained and SD link-unaware optimal rules considered in the literature.

Contemporary cellular standards, such as Long Term Evolution (LTE) and LTE-Advanced, employ orthogonal frequency-division multiplexing (OFDM) and use frequency-domain scheduling and rate adaptation. In conjunction with feedback reduction schemes, high downlink spectral efficiencies are achieved while limiting the uplink feedback overhead. One such important scheme that has been adopted by these standards is best- m feedback, in which every user feeds back its m largest subchannel (SC) power gains and their corresponding indices. We analyze the single cell average throughput of an OFDM system with uniformly correlated SC gains that employs best- m feedback and discrete rate adaptation. Our model incorporates three schedulers that cover a wide range of the throughput versus fairness tradeoff and feedback delay. We show that, for small m, correlation significantly reduces average throughput with best- m feedback. This result is pertinent as even in typical dispersive channels, correlation is high. We observe that the schedulers exhibit varied sensitivities to correlation and feedback delay. The analysis also leads to insightful expressions for the average throughput in the asymptotic regime of a large number of users.

Cooperative relaying combined with selection exploits spatial diversity to significantly improve the performance of interference-constrained secondary users in an underlay cognitive radio (CR) network. However, unlike conventional relaying, the state of the links between the relay and the primary receiver affects the choice of the relay. Further, while the optimal amplify-and-forward (AF) relay selection rule for underlay CR is well understood for the peak interference-constraint, this is not so for the less conservative average interference constraint. For the latter, we present three novel AF relay selection (RS) rules, namely, symbol error probability (SEP)-optimal, inverse-of-affine (IOA), and linear rules. We analyze the SEPs of the IOA and linear rules and also develop a novel, accurate approximation technique for analyzing the performance of AF relays. Extensive numerical results show that all the three rules outperform several RS rules proposed in the literature and generalize the conventional AF RS rule.

Opportunistic selection in multi-node wireless systems improves system performance by selecting the “best” node and by using it for data transmission. In these systems, each node has a real-valued local metric, which is a measure of its ability to improve system performance. Our goal is to identify the best node, which has the largest metric. We propose, analyze, and optimize a new distributed, yet simple, node selection scheme that combines the timer scheme with power control. In it, each node sets a timer and transmit power level as a function of its metric. The power control is designed such that the best node is captured even if η other nodes simultaneously transmit with it. We develop several structural properties about the optimal metric-to-timer-and-power mapping, which maximizes the probability of selecting the best node. These significantly reduce the computational complexity of finding the optimal mapping and yield valuable insights about it. We show that the proposed scheme is scalable and significantly outperforms the conventional timer scheme. We investigate the effect of η and the number of receive power levels. Furthermore, we find that the practical peak power constraint has a negligible impact on the performance of the scheme.

In contemporary orthogonal frequency division multiplexing (OFDM) systems, such as Long Term Evolution (LTE), LTE-Advanced, and WiMAX, a codeword is transmitted over a group of subcarriers. Since different subcarriers see different channel gains in frequency-selective channels, the modulation and coding scheme (MCS) of the codeword must be selected based on the vector of signal-to-noise-ratios (SNRs) of these subcarriers. Exponential effective SNR mapping (EESM) maps the vector of SNRs into an equivalent flat-fading SNR, and is widely used to simplify this problem. We develop a new analytical framework to characterize the throughput of EESM-based rate adaptation in such wideband channels in the presence of feedback delays. We derive a novel accurate approximation for the throughput as a function of feedback delay. We also propose a novel bivariate gamma distribution to model the time evolution of EESM between the times of estimation and data transmission, which facilitates the analysis. These are then generalized to a multi-cell, multi-user scenario with various frequency-domain schedulers. Unlike prior work, most of which is simulation-based, our framework encompasses both correlated and independent subcarriers and various multiple antenna diversity modes; it is accurate over a wide range of delays.

In a system with energy harvesting (EH) nodes, the design focus shifts from minimizing energy consumption by infrequently transmitting less information to making the best use of available energy to efficiently deliver data while adhering to the fundamental energy neutrality constraint. We address the problem of maximizing the throughput of a system consisting of rate-adaptive EH nodes that transmit to a destination. Unlike related literature, we focus on the practically important discrete-rate adaptation model. First, for a single EH node, we propose a discrete-rate adaptation rule and prove its optimality for a general class of stationary and ergodic EH and fading processes. We then study a general system with multiple EH nodes in which one is opportunistically selected to transmit. We first derive a novel and throughput-optimal joint selection and rate adaptation rule (TOJSRA) when the nodes are subject to a weaker average power constraint. We then propose a novel rule for a multi-EH node system that is based on TOJSRA, and we prove its optimality for stationary and ergodic EH and fading processes. We also model the various energy overheads of the EH nodes and characterize their effect on the adaptation policy and the system throughput.

Computing the maximum of sensor readings arises in several environmental, health, and industrial monitoring applications of wireless sensor networks (WSNs). We characterize the several novel design trade-offs that arise when green energy harvesting (EH) WSNs, which promise perpetual lifetimes, are deployed for this purpose. The nodes harvest renewable energy from the environment for communicating their readings to a fusion node, which then periodically estimates the maximum. For a randomized transmission schedule in which a pre-specified number of randomly selected nodes transmit in a sensor data collection round, we analyze the mean absolute error (MAE), which is defined as the mean of the absolute difference between the maximum and that estimated by the fusion node in each round. We optimize the transmit power and the number of scheduled nodes to minimize the MAE, both when the nodes have channel state information (CSI) and when they do not. Our results highlight how the optimal system operation depends on the EH rate, availability and cost of acquiring CSI, quantization, and size of the scheduled subset. Our analysis applies to a general class of sensor reading and EH random processes.

In orthogonal frequency division multiplexing (OFDM) systems, such as long term evolution (LTE) and WiMAX, a codeword is transmitted over a group of subcarriers. Since the subcarriers see different channel gains in a frequency-selective channel, the modulation and coding scheme (MCS) of the codeword must be selected based on the vector of signal-to-noise-ratios (SNRs) of these subcarriers. Exponential effective SNR mapping (EESM) simplifies this problem by mapping the vector of SNRs into a single, equivalent flat-fading SNR. We develop a new analytical framework to characterize the throughput of EESM-based rate adaptation in such wideband channels in the presence of feedback delays, which make the choice of the MCS partially outdated by the time data transmission takes place. To this end, we first propose a novel bivariate gamma distribution to model the joint statistics of EESM at the times of estimation and data transmission. We then derive a novel expression for the throughput as a function of feedback delay. Our framework works for both correlated and independent subcarriers and for various multiple antenna diversity modes, and is accurate over a wide range of delays.

In several wireless sensor networks, it is of interest to determine the maximum of the sensor readings and identify the sensor responsible for it. This has been referred to as the max function computation problem in the literature. We propose a novel, decentralized, timer-based max function computation (TMC) algorithm. In it, the sensors do not transmit their readings in a centrally pre-defined sequence. Instead, they are divided into clusters. The computation occurs over two stages. In the first stage, the nodes contend with each other using a decentralized timer scheme to transmit their reading to their cluster heads. In the second stage, the cluster heads contend in a similar manner. The main challenge that arises with the use of the timer scheme is the possibility of collisions, which can make the algorithm fail in finding the maximum. We optimize the algorithm to minimize the average time required to determine the maximum subject to a constraint on the probability that it fails to find it due to collisions. Extensive benchmarking shows that TMC requires lower selection times and far fewer transmissions on average than other approaches proposed in the literature.

A relay that operates in an underlay cognitive radio (CR) system is subject to tight constraints on the interference its transmissions cause to the primary receiver (PRx). While several appealing non-regenerative amplify-and-forward (AF) relaying schemes have been proposed for underlay CR, they are simple, ad hoc adaptations of conventional AF relaying schemes. We present a novel and optimal relay gain adaptation policy (ORGAP) in which the interference-aware relay optimally adapts its gain as a function of its local channel gains. It minimizes the symbol error probability (SEP) at the secondary receiver subject to a constraint on the average interference caused to the PRx. We also analyze the SEP of MPSK of ORGAP, which serves as a fundamental theoretical benchmark for the gains achievable by AF relaying in CR systems. Extensive numerical results quantify the extent to which ORGAP outperforms several known conventional AF relaying schemes. We also present a near-optimal, simpler relay gain adaptation policy (SRGAP) that is easier to implement.

Opportunistic selection selects the node that improves the overall system performance the most. Selecting the best node is challenging as the nodes are geographically distributed and have only local knowledge. Yet, selection must be fast to allow more time to be spent on data transmission, which exploits the selected node's services. We analyze the impact of imperfect power control on a fast, distributed, splitting based selection scheme that exploits the capture effect by allowing the transmitting nodes to have different target receive powers and uses information about the total received power to speed up selection. Imperfect power control makes the received power deviate from the target and, hence, affects performance. Our analysis quantifies how it changes the selection probability, reduces the selection speed, and leads to the selection of no node or a wrong node. We show that the effect of imperfect power control is primarily driven by the ratio of target receive powers. Furthermore, we quantify its effect on the net system throughput.

Adapting the power of secondary users (SUs) while adhering to constraints on the interference caused to primary receivers (PRxs) is a critical issue in underlay cognitive radio (CR). This adaptation is driven by the interference and transmit power constraints imposed on the secondary transmitter (STx). Its performance also depends on the quality of channel state information (CSI) available at the STx of the links from the STx to the secondary receiver and to the PRxs. For a system in which an STx is subject to an average interference constraint or an interference outage probability constraint at each of the PRxs, we derive novel symbol error probability (SEP)-optimal, practically motivated binary transmit power control policies. As a reference, we also present the corresponding SEP-optimal continuous transmit power control policies for one PRx. We then analyze the robustness of the optimal policies when the STx knows noisy channel estimates of the links between the SU and the PRxs. Altogether, our work develops a holistic understanding of the critical role played by different transmit and interference constraints in driving power control in underlay CR and the impact of CSI on its performance.

In an underlay cognitive radio (CR) system, a secondary user can transmit when the primary is transmitting but is subject to tight constraints on the interference it causes to the primary receiver. Amplify-and-forward (AF) relaying is an effective technique that significantly improves the performance of a CR by providing an alternate path for the secondary transmitter's signal to reach the secondary receiver. We present and analyze a novel optimal relay gain adaptation policy (ORGAP) in which the relay is interference aware and optimally adapts both its gain and transmit power as a function of its local channel gains. ORGAP minimizes the symbol error probability at the secondary receiver subject to constraints on the average relay transmit power and on the average interference caused to the primary. It is different from ad hoc AF relaying policies and serves as a new and fundamental theoretical benchmark for relaying in an underlay CR. We also develop a near-optimal and simpler relay gain adaptation policy that is easy to implement. An extension to a multirelay scenario with selection is also developed. Our extensive numerical results for single and multiple relay systems quantify the power savings achieved over several ad hoc policies for both MPSK and MQAM constellations.

The performance of an underlay cognitive radio (CR) system, which can transmit when the primary is on, is curtailed by tight constraints on the interference it can cause to the primary receiver. Transmit antenna selection (AS) improves the performance of underlay CR by exploiting spatial diversity but with less hardware. However, the selected antenna and its transmit power now both depend on the channel gains to the secondary and primary receivers. We develop a novel Chernoff-bound based optimal AS and power adaptation (CBBOASPA) policy that minimizes an upper bound on the symbol error probability (SEP) at the secondary receiver, subject to constraints on the average transmit power and the average interference to the primary. The optimal antenna and its power are presented in an insightful closed form in terms of the channel gains. We then analyze the SEP of CBBOASPA. Extensive benchmarking shows that the SEP of CBBOASPA for both MPSK and MQAM is one to two orders of magnitude lower than several ad hoc AS policies and even optimal AS with on-off power control.

Accurately characterizing the time-varying interference caused to the primary users is essential in ensuring a successful deployment of cognitive radios (CR). We show that the aggregate interference at the primary receiver (PU-Rx) from multiple, randomly located cognitive users (CUs) is well modeled as a shifted lognormal random process, which is more accurate than the lognormal and the Gaussian process models considered in the literature, even for a relatively dense deployment of CUs. It also compares favorably with the asymptotically exact stable and symmetric truncated stable distribution models, except at high CU densities. Our model accounts for the effect of imperfect spectrum sensing, which depends on path-loss, shadowing, and small-scale fading of the link from the primary transmitter to the CU; the interweave and underlay modes of CR operation, which determine the transmit powers of the CUs; and time-correlated shadowing and fading of the links from the CUs to the PU-Rx. It leads to expressions for the probability distribution function, level crossing rate, and average exceedance duration. The impact of cooperative spectrum sensing is also characterized. We validate the model by applying it to redesign the primary exclusive zone to account for the time-varying nature of interference.

In contemporary wideband orthogonal frequency division multiplexing (OFDM) systems, such as Long Term Evolution (LTE) and WiMAX, different subcarriers over which a codeword is transmitted may experience different signal-to-noise-ratios (SNRs). Thus, adaptive modulation and coding (AMC) in these systems is driven by a vector of subcarrier SNRs experienced by the codeword, and is more involved. Exponential effective SNR mapping (EESM) simplifies the problem by mapping this vector into a single equivalent flat-fading SNR. Analysis of AMC using EESM is challenging owing to its non-linear nature and its dependence on the modulation and coding scheme. We first propose a novel statistical model for the EESM, which is based on the Beta distribution. It is motivated by the central limit approximation for random variables with a finite support. It is simpler and as accurate as the more involved ad hoc models proposed earlier. Using it, we develop novel expressions for the throughput of a point-to-point OFDM link with multi-antenna diversity that uses EESM for AMC. We then analyze a general, multi-cell OFDM deployment with co-channel interference for various frequency-domain schedulers. Extensive results based on LTE and WiMAX are presented to verify the model and analysis, and gain new insights.

Energy harvesting (EH) is an attractive and green solution to the problem of limited lifetime of wireless sensor networks (WSNs). Unlike a conventional node that dies once it runs out of energy, an EH node harvests energy from the environment and replenishes its rechargeable battery. We investigate a new class of hybrid networks that comprise both EH and conventional nodes and differ from conventional and all-EH WSNs. We propose two new and insightful performance criteria called k-outage duration and n-transmission duration to evaluate these networks. They overcome the pitfalls associated with defining lifetime, which arise because the EH nodes never die but can occasionally run out of energy, and capture the dynamic time evolution, which occurs because the conventional nodes irreversibly drain their batteries. They also account for the inability of the nodes to transmit data due to insufficient battery energy and channel fading. We prove two computationally efficient novel bounds for evaluating these criteria. Our results characterize the effect of the number of EH and conventional nodes and channel fading statistics on these criteria. Further, given a total cost constraint, we determine the conventional and EH node mixture in the network that optimizes these criteria.

Accurately characterizing the time-varying nature of the aggregate interference from secondary users (SUs) is essential in ensuring a successful deployment of a cognitive radio (CR) network. This requires characterizing the probability distribution and the time-varying nature of the aggregate interference from multiple SUs. We show that it is well modeled as a shifted lognormal random process, and is more accurate than the lognormal, Gaussian, and symmetric truncated stable models considered in the literature even for a relatively dense deployment of SUs. Our model accounts for the effect of imperfect spectrum sensing, which depends on path loss, shadowing, and fading of the link from primary transmitter to the SU, and the randomness in the number of SUs and their locations. It also allows for both interweave and underlay modes of CR operation. We also demonstrate the relevance of the proposed analytically tractable model in the design of the primary exclusive zone.

In orthogonal frequency division multiplexing systems, such as Long Term Evolution (LTE) and WiMAX, the different subcarriers over which a codeword is transmitted may see different signal-to-noise-ratios (SNRs). Thus, adaptive modulation and coding (AMC) in these systems must be based on a vector of subcarrier SNRs seen by the codeword, and is considerably more involved. Exponential effective SNR mapping (EESM) simplifies the problem by mapping the vector of SNRs into a single equivalent flat-fading SNR. However, the analysis of AMC using EESM is challenging owing to its non-linear nature and because it uses an SNR scaling parameter that depends on the modulation and coding scheme. We first propose a novel statistical model for EESM based on the Beta distribution, which is motivated by the central limit approximation for the sum of random variables with finite support. Unlike several ad hoc statistical models, which require three or more parameters to be computed numerically, the proposed model requires only two parameters, for which closed-form expressions are derived for both correlated and uncorrelated subcarrier SNRs. Despite its simplicity, it is as accurate as the ad hoc models. We then present a novel, tight upper bound and an accurate approximation in closed-form for the throughput of a frequency-selective system that uses EESM for AMC.

In an underlay cognitive radio (CR) system, a secondary user (SU) can transmit even when the primary is on but under stringent constraints on the interference that it causes at the primary receiver (PRx). The interference constraint fundamentally influences and changes how the SU transmits. We develop a novel and optimal transmit power policy for an SU that minimizes its symbol error probability (SEP) when it is subject to two practically motivated constraints, namely, a peak transmit power constraint and an interference outage probability constraint. We derive new expressions for the SEP of the optimal transmit power policy for MPSK. Our results bring out the impact of several system parameters such as the peak transmit power, the target outage probability, the interference threshold, and the constellation size on the SEP of the CR system.

Multiple relay selection enables a cooperative system to obtain better performance than single relay selection and yet avoid challenging problems such as synchronization that are associated with having all the relays transmit. While its benefits have been well characterized, the problem of developing distributed, scalable schemes that discover the best subset of relays remains to be fully investigated. The problem is challenging because the relays are spatially separated from each other and have only local channel knowledge. We investigate the popular, low feedback, and distributed timer scheme and derive a novel, optimal timer mapping that maximizes the probability of selecting the best two relays. This has applications in several cooperative schemes proposed in the literature. We derive several novel structural properties about the optimal mapping, which reduce the complexity of finding it from the large space of all functions to a one-dimensional search that can be solved using a computationally efficient, iterative algorithm. Our extensive benchmarking shows that the optimal mapping outperforms several relay discovery schemes proposed in the literature. The approach can be generalized to selecting the best l relays, as well.

Opportunistic selection aims to select a node that improves the overall system performance the most. Selection is challenging as the nodes are geographically distributed and have only local knowledge. Yet, selection needs to be fast in order to allocate more time to the data transmission phase that exploits the selected node's services. In this paper, we analyze the impact of imperfect power control on a fast, distributed, splitting-based selection scheme that exploits the capture effect by allowing the transmitting nodes to have different target receive powers and uses information about the total received power to speed up selection. The scheme owes its speed to the use of different target powers that facilitate capture. However, imperfect power control makes the received power deviate from the target and, hence, affects performance. Our analysis quantifies how it changes the selection speed, leads to the selection of wrong node, or no node getting selected. We also quantify the effect of imperfect power control on the net system throughput and the extent of error beyond which power control is not useful.

Opportunistic relay selection in a multiple source-destination (MSD) cooperative system involves allocating to each source-destination (SD) pair a relay based on its channel gains. Since each node in the system knows only its local channel gains, a relay selection algorithm is required to quickly identify and assign the best relay to each SD pair. For an MSD system in which the SD pairs communicate in a time-orthogonal manner, we propose two new relay selection algorithms, namely, contention-free en masse assignment (CFEA) and contention-based en masse assignment (CBEA). En masse assignment exploits the fact that in an MSD system a relay can often aid not one but multiple SD pairs, and, therefore, can be assigned multiple SD pairs en masse. We show that CFEA and CBEA require much less time to allocate an SD pair than in single SD systems, and achieve a higher net throughput in several regimes of interest when compared with other selection algorithms proposed in the literature. We also identify the regimes in which CFEA is better than CBEA and vice versa.

Energy harvesting sensor (EHS) nodes provide an attractive and green solution to the problem of limited lifetime of wireless sensor networks (WSNs). Unlike a conventional node that uses a non-rechargeable battery and dies once it runs out of energy, an EHS node can harvest energy from the environment and replenish its rechargeable battery. We consider hybrid WSNs that comprise of both EHS and conventional nodes; these arise when legacy WSNs are upgraded or due to EHS deployment cost issues. We compare conventional and hybrid WSNs on the basis of a new and insightful performance metric called k-outage duration, which captures the inability of the nodes to transmit data either due to lack of sufficient battery energy or wireless fading. The metric overcomes the problem of defining lifetime in networks with EHS nodes, which never die but are occasionally unable to transmit due to lack of sufficient battery energy. It also accounts for the effect of wireless channel fading on the ability of the WSN to transmit data. We develop two novel, tight, and computationally simple bounds for evaluating the k-outage duration. Our results show that increasing the number of EHS nodes has a markedly different effect on the k-outage duration than increasing the number of conventional nodes.

Transmit antenna selection (AS) is a popular, low hardware complexity technique that improves the performance of an underlay cognitive radio system, in which a secondary transmitter can transmit when the primary is on but under tight constraints on the interference it causes to the primary. The underlay interference constraint fundamentally changes the criterion used to select the antenna because the channel gains to the secondary and primary receivers must be both taken into account. We develop a novel and optimal joint AS and transmit power adaptation policy that minimizes a Chernoff upper bound on the symbol error probability (SEP) at the secondary receiver subject to an average transmit power constraint and an average primary interference constraint. Explicit expressions for the optimal antenna and power are provided in terms of the channel gains to the primary and secondary receivers. The SEP of the optimal policy is at least an order of magnitude lower than that achieved by several ad hoc selection rules proposed in the literature and even the optimal antenna selection rule for the case where the transmit power is either zero or a fixed value.

Given the significant gains that relay-based cooperation promises, the practical problems of acquisition of channel state information (CSI) and the characterization and optimization of performance with imperfect CSI are receiving increasing attention. We develop novel and accurate expressions for the symbol error probability (SEP) for fixed-gain amplify-and-forward relaying when the destination acquires CSI using the time-efficient cascaded channel estimation (CCE) protocol. The CCE protocol saves time by making the destination directly estimate the product of the source-relay and relay-destination channel gains. For a single relay system, we first develop a novel SEP expression and a tight SEP upper bound. We then similarly analyze an opportunistic multi-relay system, in which both selection and coherent demodulation use imperfect estimates. A distinctive aspect of our approach is the use of as few simplifying approximations as possible, which results in new results that are accurate at signal-to-noise-ratios as low as 1 dB for single and multi-relay systems. Using insights gleaned from an asymptotic analysis, we also present a simple, closed-form, nearly-optimal solution for allocation of energy between pilot and data symbols at the source and relay(s).

Opportunistic relay selection in a multiple source-destination (MSD) cooperative system requires quickly allocating to each source-destination (SD) pair a suitable relay based on channel gains. Since the channel knowledge is available only locally at a relay and not globally, efficient relay selection algorithms are needed. For an MSD system, in which the SD pairs communicate in a time-orthogonal manner with the help of decode-and-forward relays, we propose three novel relay selection algorithms, namely, contention-free en masse assignment (CFEA), contention-based en masse assignment (CBEA), and a hybrid algorithm that combines the best features of CFEA and CBEA. En masse assignment exploits the fact that a relay can often aid not one but multiple SD pairs, and, therefore, can be assigned to multiple SD pairs. This drastically reduces the average time required to allocate an SD pair when compared to allocating the SD pairs one by one. We show that the algorithms are much faster than other selection schemes proposed in the literature and yield significantly higher net system throughputs. Interestingly, CFEA is as effective as CBEA over a wider range of system parameters than in single SD pair systems.

Single receive antenna selection (AS) is a popular method for obtaining diversity benefits without the additional costs of multiple radio receiver chains. Since only one antenna receives at any time, the transmitter sends a pilot multiple times to enable the receiver to estimate the channel gains of its N antennas to the transmitter and select an antenna. In time-varying channels, the channel estimates of different antennas are outdated to different extents. We analyze the symbol error probability (SEP) in time-varying channels of the N-pilot and (N + 1)-pilot AS training schemes. In the former, the transmitter sends one pilot for each receive antenna. In the latter, the transmitter sends one additional pilot that helps sample the channel fading process of the selected antenna twice. We present several new results about the SEP, optimal energy allocation across pilots and data, and optimal selection rule in time-varying channels for the two schemes. We show that due to the unique nature of AS, the (N +1)-pilot scheme, despite its longer training duration, is much more energy-efficient than the conventional N-pilot scheme. An extension to a practical scenario where all data symbols of a packet are received by the same antenna is also investigated.

An opportunistic, rate-adaptive system exploits multi-user diversity by selecting the best node, which has the highest channel power gain, and adapting the data rate to selected node's channel gain. Since channel knowledge is local to a node, we propose using a distributed, low-feedback timer backoff scheme to select the best node. It uses a mapping that maps the channel gain, or, in general, a real-valued metric, to a timer value. The mapping is such that timers of nodes with higher metrics expire earlier. Our goal is to maximize the system throughput when rate adaptation is discrete, as is the case in practice. To improve throughput, we use a pragmatic selection policy, in which even a node other than the best node can be selected. We derive several novel, insightful results about the optimal mapping and develop an algorithm to compute it. These results bring out the inter-relationship between the discrete rate adaptation rule, optimal mapping, and selection policy. We also extensively benchmark the performance of the optimal mapping with several timer and opportunistic multiple access schemes considered in the literature, and demonstrate that the developed scheme is effective in many regimes of interest.

In the underlay mode of cognitive radio, secondary users are allowed to transmit when the primary is transmitting, but under tight interference constraints that protect the primary. However, these constraints limit the secondary system performance. Antenna selection (AS)-based multiple antenna techniques, which exploit spatial diversity with less hardware, help improve secondary system performance. We develop a novel and optimal transmit AS rule that minimizes the symbol error probability (SEP) of an average interference-constrained multiple-input-single-output secondary system that operates in the underlay mode. We show that the optimal rule is a non-linear function of the power gain of the channel from the secondary transmit antenna to the primary receiver and from the secondary transmit antenna to the secondary receive antenna. We also propose a simpler, tractable variant of the optimal rule that performs as well as the optimal rule. We then analyze its SEP with \tL transmit antennas, and extensively benchmark it with several heuristic selection rules proposed in the literature. We also enhance these rules in order to provide a fair comparison, and derive new expressions for their SEPs. The results bring out new inter-relationships between the various rules, and show that the optimal rule can significantly reduce the SEP.

The distributed, low-feedback, timer scheme is used in several wireless systems to select the best node from the available nodes. In it, each node sets a timer as a function of a local preference number called a metric, and transmits a packet when its timer expires. The scheme ensures that the timer of the best node, which has the highest metric, expires first. However, it fails to select the best node if another node transmits a packet within Δ s of the transmission by the best node. We derive the optimal metric-to-timer mappings for the practical scenario where the number of nodes is unknown. We consider two cases in which the probability distribution of the number of nodes is either known a priori or is unknown. In the first case, the optimal mapping maximizes the success probability averaged over the probability distribution. In the second case, a robust mapping maximizes the worst case average success probability over all possible probability distributions on the number of nodes. Results reveal that the proposed mappings deliver significant gains compared to the mappings considered in the literature.

Transmit antenna selection (AS) has been adopted in contemporary wideband wireless standards such as Long Term Evolution (LTE). We analyze a comprehensive new model for AS that captures several key features about its operation in wideband orthogonal frequency division multiple access (OFDMA) systems. These include the use of channel-aware frequency-domain scheduling (FDS) in conjunction with AS, the hardware constraint that a user must transmit using the same antenna over all its assigned subcarriers, and the scheduling constraint that the subcarriers assigned to a user must be contiguous. The model also captures the novel dual pilot training scheme that is used in LTE, in which a coarse system bandwidth-wide sounding reference signal is used to acquire relatively noisy channel state information (CSI) for AS and FDS, and a dense narrow-band demodulation reference signal is used to acquire accurate CSI for data demodulation. We analyze the symbol error probability when AS is done in conjunction with the channel-unaware, but fair, round-robin scheduling and with channel-aware greedy FDS. Our results quantify how effective joint AS-FDS is in dispersive environments, the interactions between the above features, and the ability of the user to lower SRS power with minimal performance degradation.

In underlay cognitive radio (CR), a secondary user (SU) can transmit concurrently with a primary user (PU) provided that it does not cause excessive interference at the primary receiver (PRx). The interference constraint fundamentally changes how the SU transmits, and makes link adaptation in underlay CR systems different from that in conventional wireless systems. In this paper, we develop a novel, symbol error probability (SEP)-optimal transmit power adaptation policy for an underlay CR system that is subject to two practically motivated constraints, namely, a peak transmit power constraint and an interference outage probability constraint. For the optimal policy, we derive its SEP and a tight upper bound for MPSK and MQAM constellations when the links from the secondary transmitter (STx) to its receiver and to the PRx follow the versatile Nakagami-m fading model. We also characterize the impact of imperfectly estimating the STx-PRx link on the SEP and the interference. Extensive simulation results are presented to validate the analysis and evaluate the impact of the constraints, fading parameters, and imperfect estimates.

Multi-packet reception (MPR) promises significant throughput gains in wireless local area networks (WLANs) by allowing nodes to transmit even in the presence of ongoing transmissions in the medium. However, the medium access control (MAC) layer must now be redesigned to facilitate - rather than discourage - these overlapping transmissions. We investigate asynchronous MPR MAC protocols, which successfully accomplish this by controlling the node behavior based on the number of ongoing transmissions in the channel. The protocols use the backoff timer mechanism of the distributed coordination function, which makes them practically appealing. We first highlight a unique problem of acknowledgment delays, which arises in asynchronous MPR, and investigate a solution that modifies the medium access rules to reduce these delays and increase system throughput in the single receiver scenario. We develop a general renewal-theoretic fixed-point analysis that leads to expressions for the saturation throughput, packet dropping probability, and average head-of-line packet delay. We also model and analyze the practical scenario in which nodes may incorrectly estimate the number of ongoing transmissions.

This paper addresses the problem of finding optimal power control policies for wireless energy harvesting sensor (EHS) nodes with automatic repeat request (ARQ)-based packet transmissions. The EHS harvests energy from the environment according to a Bernoulli process; and it is required to operate within the constraint of energy neutrality. The EHS obtains partial channel state information (CSI) at the transmitter through the link-layer ARQ protocol, via the ACK/NACK feedback messages, and uses it to adapt the transmission power for the packet (re)transmission attempts. The underlying wireless fading channel is modeled as a finite state Markov chain with known transition probabilities. Thus, the goal of the power management policy is to determine the best power setting for the current packet transmission attempt, so as to maximize a long-run expected reward such as the expected outage probability. The problem is addressed in a decision-theoretic framework by casting it as a partially observable Markov decision process (POMDP). Due to the large size of the state-space, the exact solution to the POMDP is computationally expensive. Hence, two popular approximate solutions are considered, which yield good power management policies for the transmission attempts. Monte Carlo simulation results illustrate the efficacy of the approach and show that the approximate solutions significantly outperform conventional approaches.

Orthogonal frequency division multiple access (OFDMA) systems exploit multiuser diversity and frequency-selectivity to achieve high spectral efficiencies. However, they require considerable feedback for scheduling and rate adaptation, and are sensitive to feedback delays. We develop a comprehensive analysis of the OFDMA system throughput as a function of the feedback scheme, frequency-domain scheduler, and discrete rate adaptation rule in the presence of feedback delays. We analyze the popular best-n and threshold-based feedback schemes. We show that for both the greedy and round-robin schedulers, the throughput degradation, given a feedback delay, depends primarily on the fraction of feedback reduced by the feedback scheme and not the feedback scheme itself. Even small feedback delays at low vehicular speeds are shown to significantly degrade the throughput. We also show that optimizing the link adaptation thresholds as a function of the feedback delay can effectively counteract the detrimental effect of delays.

Multi-packet reception (MPR), in which a receiver can decode multiple simultaneous transmissions, significantly improves the uplink throughput of wireless local area networks (WLANs). However, the medium access control (MAC) layer must be redesigned to encourage, and not avoid, simultaneous transmissions. Asynchronous MPR MAC protocols, in which nodes independently access the channel so long as the number of ongoing transmissions is less than a threshold, are promising solutions for enabling MPR in IEEE 802.11-based WLANs. In this paper, we highlight the problem of acknowledgment (ACK) delays that arises in asynchronous MPR when multiple nodes transmit in succession without the channel becoming idle. We propose a novel asynchronous MAC protocol that reduces the ACK delays, increases throughput, and retains the distributed nature of the 802.11 distributed coordination function (DCF). An accurate renewal theoretic fixed-point analysis that leads to general analytical expressions for the saturation throughput is also developed.

In the underlay mode of cognitive radio, secondary users can transmit when the primary is transmitting, but under tight interference constraints, which limit the secondary system performance. Antenna selection (AS)-based multiple antenna techniques, which require less hardware and yet exploit spatial diversity, help improve the secondary system performance. In this paper, we develop the optimal transmit AS rule that minimizes the symbol error probability (SEP) of an average interference-constrained secondary system that operates in the underlay mode. We show that the optimal rule is a non-linear function of the power gains of the channels from secondary transmit antenna to primary receiver and secondary transmit antenna to secondary receive antenna. The optimal rule is different from the several ad hoc rules that have been proposed in the literature. We also propose a closed-form, tractable variant of the optimal rule and analyze its SEP. Several results are presented to compare the performance of the closed-form rule with the ad hoc rules, and interesting inter-relationships among them are brought out.

Single receive antenna selection (AS) allows single-input single-output (SISO) systems to retain the diversity benefits of multiple antennas with minimum hardware costs. We propose a single receive AS method for time-varying channels, in which practical limitations imposed by next-generation wireless standards such as training, packetization and antenna switching time are taken into account. The proposed method utilizes low-complexity subspace projection techniques spanned by discrete prolate spheroidal (DPS) sequences. It only uses Doppler bandwidth knowledge, and does not need detailed correlation knowledge. Results show that the proposed AS method outperforms ideal conventional SISO systems with perfect CSI but no AS at the receiver and AS using the conventional Fourier estimation/prediction method. A closed-form expression for the symbol error probability (SEP) of phase-shift keying (MPSK) with symbol-by-symbol receive AS is derived.

Channel-aware assignment of subchannels to users in the downlink of an OFDMA system requires extensive feedback of channel state information (CSI) to the base station. Since bandwidth is scarce, schemes that limit feedback are necessary. We develop a novel, low feedback, distributed splitting-based algorithm called SplitSelect to opportunistically assign each subchannel to its most suitable user. SplitSelect explicitly handles multiple access control aspects associated with CSI feedback, and scales well with the number of users. In it, according to a scheduling criterion, each user locally maintains a scheduling metric for each subchannel. The goal is to select, for each subchannel, the user with the highest scheduling metric. At any time, each user contends for the subchannel for which it has the largest scheduling metric among the unallocated subchannels. A tractable asymptotic analysis of a system with many users is central to SplitSelect's simple design. Extensive simulation results demonstrate the speed with which subchannels and users are paired. The net data throughput, when the time overhead of selection is accounted for, is shown to be substantially better than several schemes proposed in the literature. We also show how fairness and user prioritization can be ensured by suitably defining the scheduling metric.

In a communication system in which K nodes communicate with a central sink node, the following problem of selection often occurs. Each node maintains a preference number called a metric, which is not known to other nodes. The sink node must find the `best' node with the largest metric. The local nature of the metrics requires the selection process to be distributed. Further, the selection needs to be fast in order to increase the fraction of time available for data transmission using the selected node and to handle time-varying environments. While several selection schemes have been proposed in the literature, each has its own shortcomings. We propose a novel, distributed selection scheme that generalizes the best features of the timer scheme, which requires minimal feedback but does not guarantee successful selection, and the splitting scheme, which requires more feedback but guarantees successful selection. The proposed scheme introduces several new ideas into the design of the timer and splitting schemes. It explicitly accounts for feedback overheads and guarantees selection of the best node. We analyze and optimize the performance of the scheme and show that it is scalable, reliable, and fast. We also present new insights about the optimal timer scheme.

Receive antenna selection (AS) has been shown to maintain the diversity benefits of multiple antennas while potentially reducing hardware costs. However, the promised diversity gains of receive AS depend on the assumptions of perfect channel knowledge at the receiver and slowly time-varying fading. By explicitly accounting for practical constraints imposed by the next-generation wireless standards such as training, packetization and antenna switching time, we propose a single receive AS method for time-varying fading channels. The method exploits the low training overhead and accuracy possible from the use of discrete prolate spheroidal (DPS) sequences based reduced rank subspace projection techniques. It only requires knowledge of the Doppler bandwidth, and does not require detailed correlation knowledge. Closed-form expressions for the channel prediction and estimation error as well as symbol error probability (SEP) of M-ary phase-shift keying (MPSK) for symbol-by-symbol receive AS are also derived. It is shown that the proposed AS scheme, after accounting for the practical limitations mentioned above, outperforms the ideal conventional single-input single-output (SISO) system with perfect CSI and no AS at the receiver and AS with conventional estimation based on complex exponential basis functions.

The throughput-optimal discrete-rate adaptation policy, when nodes are subject to constraints on the average power and bit error rate, is governed by a power control parameter, for which a closed-form characterization has remained an open problem. The parameter is essential in determining the rate adaptation thresholds and the transmit rate and power at any time, and ensuring adherence to the power constraint. We derive novel insightful bounds and approximations that characterize the power control parameter and the throughput in closed-form. The results are comprehensive as they apply to the general class of Nakagami-m (m ≥1) fading channels, which includes Rayleigh fading, uncoded and coded modulation, and single and multi-node systems with selection. The results are appealing as they are provably tight in the asymptotic large average power regime, and are designed and verified to be accurate even for smaller average powers.

Two models for AF relaying, namely, fixed gain and fixed power relaying, have been extensively studied in the literature given their ability to harness spatial diversity. In fixed gain relaying, the relay gain is fixed but its transmit power varies as a function of the source-relay channel gain. In fixed power relaying, the relay transmit power is fixed, but its gain varies. We revisit and generalize the fundamental two-hop AF relaying model. We present an optimal scheme in which an average power constrained AF relay adapts its gain and transmit power to minimize the symbol error probability (SEP) at the destination. Also derived are insightful and practically amenable closed-form bounds for the optimal relay gain. We then analyze the SEP of MPSK, derive tight bounds for it, and characterize the diversity order for Rayleigh fading. Also derived is an SEP approximation that is accurate to within 0.1 dB. Extensive results show that the scheme yields significant energy savings of 2.0-7.7 dB at the source and relay. Optimal relay placement for the proposed scheme is also characterized, and is different from fixed gain or power relaying. Generalizations to MQAM and other fading distributions are also discussed.

In a cooperative system with an amplify-and-forward relay, the cascaded channel training protocol enables the destination to estimate the source-destination channel gain and the product of the source-relay (SR) and relay-destination (RD) channel gains using only two pilot transmissions from the source. Notably, the destination does not require a separate estimate of the SR channel. We develop a new expression for the symbol error probability (SEP) of AF relaying when imperfect channel state information (CSI) is acquired using the above training protocol. A tight SEP upper bound is also derived; it shows that full diversity is achieved, albeit at a high signal-to-noise ratio (SNR). Our analysis uses fewer simplifying assumptions, and leads to expressions that are accurate even at low SNRs and are different from those in the literature. For instance, it does not approximate the estimate of the product of SR and RD channel gains by the product of the estimates of the SR and RD channel gains. We show that cascaded channel estimation often outperforms a channel estimation protocol that incurs a greater training overhead by forwarding a quantized estimate of the SR channel gain to the destination. The extent of pilot power boosting, if allowed, that is required to improve performance is also quantified.

Opportunistic selection is a practically appealing technique that is used in multi-node wireless systems to maximize throughput, implement proportional fairness, etc. However, selection is challenging since the information about a node's channel gains is often available only locally at each node and not centrally. We propose a novel multiple access-based distributed selection scheme that generalizes the best features of the timer scheme, which requires minimal feedback but does not always guarantee successful selection, and the fast splitting scheme, which requires more feedback but guarantees successful selection. The proposed scheme's design explicitly accounts for feedback time overheads unlike the conventional splitting scheme and guarantees selection of the user with the highest metric unlike the timer scheme. We analyze and minimize the average time including feedback required by the scheme to select. With feedback overheads, the proposed scheme is scalable and considerably faster than several schemes proposed in the literature. Furthermore, the gains increase as the feedback overhead increases.

Channel-aware assignment of sub-channels to users in the downlink of an OFDMA system demands extensive feedback of channel state information (CSI) to the base station. Since the feedback bandwidth is often very scarce, schemes that limit feedback are necessary. We develop a novel, low feedback splitting-based algorithm for assigning each sub-channel to its best user, i.e., the user with the highest gain for that sub-channel among all users. The key idea behind the algorithm is that, at any time, each user contends for the sub-channel on which it has the largest channel gain among the unallocated sub-channels. Unlike other existing schemes, the algorithm explicitly handles multiple access control aspects associated with the feedback of CSI. A tractable asymptotic analysis of a system with a large number of users helps design the algorithm. It yields 50% to 65% throughput gains compared to an asymptotically optimal one-bit feedback scheme, when the number of users is as small as 10 or as large as 1000. The algorithm is fast and distributed, and scales with the number of users.

Energy Harvesting (EH) nodes, which harvest energy from the environment in order to communicate over a wireless link, promise perpetual operation of a wireless network with battery-powered nodes. In this paper, we address the throughput optimization problem for a rate-adaptive EH node that chooses its rate from a set of discrete rates and adjusts its power depending on its channel gain and battery state. First, we show that the optimal throughput of an EH node is upper bounded by the throughput achievable by a node that is subject only to an average power constraint. We then propose a simple transmission scheme for an EH node that achieves an average throughput close to the upper bound. The scheme's parameters can be made to account for energy overheads such as battery non-idealities and the energy required for sensing and processing. The effect of these overheads on the average throughput is also analytically characterized.

Spectral efficiency is a key characteristic of cellular communications systems, as it quantifies how well the scarce spectrum resource is utilized. It is influenced by the scheduling algorithm as well as the signal and interference statistics, which, in turn, depend on the propagation characteristics. In this paper we derive analytical expressions for the short-term and long-term channel-averaged spectral efficiencies of the round robin, greedy Max-SINR, and proportional fair schedulers, which are popular and cover a wide range of system performance and fairness trade-offs. A unified spectral efficiency analysis is developed to highlight the differences among these schedulers. The analysis is different from previous work in the literature in the following aspects: (i) it does not assume the co-channel interferers to be identically distributed, as is typical in realistic cellular layouts, (ii) it avoids the loose spectral efficiency bounds used in the literature, which only considered the worst case and best case locations of identical co-channel interferers, (iii) it explicitly includes the effect of multi-tier interferers in the cellular layout and uses a more accurate model for handling the total co-channel interference, and (iv) it captures the impact of using small modulation constellation sizes, which are typical of cellular standards. The analytical results are verified using extensive Monte Carlo simulations.

The Effective Exponential SNR Mapping (EESM) is an indispensable tool for analyzing and simulating next generation orthogonal frequency division multiplexing (OFDM) based wireless systems. It converts the different gains of multiple subchannels, over which a codeword is transmitted, into a single effective flat-fading gain with the same codeword error rate. It facilitates link adaptation by helping each user to compute an accurate channel quality indicator (CQI), which is fed back to the base station to enable downlink rate adaptation and scheduling. However, the highly non-linear nature of EESM makes a performance analysis of adaptation and scheduling difficult; even the probability distribution of EESM is not known in closed-form. This paper shows that EESM can be accurately modeled as a lognormal random variable when the subchannel gains are Rayleigh distributed. The model is also valid when the subchannel gains are correlated in frequency or space. With some simplifying assumptions, the paper then develops a novel analysis of the performance of LTE's two CQI feedback schemes that use EESM to generate CQI. The comprehensive model and analysis quantify the joint effect of several critical components such as scheduler, multiple antenna mode, CQI feedback scheme, and EESM-based feedback averaging on the overall system throughput.

Receive antenna selection (AS) provides many benefits of multiple-antenna systems at drastically reduced hardware costs. In it, the receiver connects a dynamically selected subset of N available antennas to the L available RF chains. Due to the nature of AS, the channel estimates at different antennas, which are required to determine the best subset for data reception, are obtained from different transmissions of the pilot sequence. Consequently, they are outdated by different amounts in a time varying channel. We show that a linear weighting of the estimates is necessary and optimum for the subset selection process, where the weights are related to the temporal correlation of the channel variations. When L is not an integer divisor of N, we highlight a new issue of "training voids", in which the last pilot transmission is not fully exploited by the receiver. We then present new "void filling" methods that exploit these voids and greatly improve the performance of AS. The optimal subset selection rules with void filling, in which different antennas turn out to have different numbers of estimates, are also explicitly characterized. Closed form equations for the symbol error probability with and without void-filling are also developed.

In a cooperative relay-assisted communication system that uses rateless codes, packets get transmitted from a source to a destination at a rate that depends on instantaneous channel states of the wireless links between nodes. When multiple relays are present, the relay with the highest channel gain to the source is the first to successfully decode a packet from the source and forward it to the destination. Thus, the unique properties of rateless codes ensure that both rate adaptation and relay selection occur without the transmitting source or relays acquiring instantaneous channel knowledge. In this paper, we show that in such cooperative systems, buffering packets at relays significantly increases throughput. We develop a novel analysis of these systems that combines the communication-theoretic aspects of cooperation over fading channels with the queuing-theoretic aspects associated with buffering. Closed-form expressions are derived for the throughput and end-to-end delay for the general case in which the channels between various nodes are not statistically identical. Corresponding results are also derived for benchmark systems that either do not exploit spatial diversity or do not buffer packets. Altogether, our results show that buffering - a capability that will be commonly available in practical deployments of relays - amplifies the benefits of cooperation.

Cooperative wireless systems can exploit spatial diversity by opportunistically selecting the best relay to forward data to a destination. However, determining the best relay is a challenging task and requires a selection algorithm because the relays are geographically separated and only have local channel knowledge. Selecting the best relay is equivalent to finding the relay with the largest metric, where each relay computes its metric using local channel knowledge. We analyze the performance of a fast, distributed, and scalable multiple access based selection algorithm when it assumes incorrect values for two fundamental parameters that it requires to operate efficiently - the number of available relays and the cumulative distribution function (CDF) of the metrics. Such imperfect knowledge will invariably arise in practice. We develop new expressions for the time required to select the best relay as a function of the assumed and actual parameters. We show that imperfect knowledge can significantly slow down the selection algorithm. Further, in a system that uses its observations to update its CDF estimate, we determine the minimum number of observations required to limit the performance degradation. We also develop a minimax formulation that makes the algorithm robust to uncertainties in the number of relays in the system.

Frequency-domain scheduling and rate adaptation have helped next generation orthogonal frequency division multiple access (OFDMA) based wireless cellular systems such as Long Term Evolution (LTE) achieve significantly higher spectral efficiencies. To overcome the severe uplink feedback bandwidth constraints, LTE uses several techniques to reduce the feedback required by a frequency-domain scheduler about the channel state information of all subcarriers of all users. In this paper, we analyze the throughput achieved by the User Selected Subband feedback scheme of LTE. In it, a user feeds back only the indices of the best M subbands and a single 4-bit estimate of the average rate achievable over all selected M subbands. In addition, we compare the performance with the subband-level feedback scheme of LTE, and highlight the role of the scheduler by comparing the performances of the unfair greedy scheduler and the proportional fair (PF) scheduler. Our analysis sheds several insights into the working of the feedback reduction techniques used in LTE.

Antenna selection (AS) provides most of the benefits of multiple-antenna systems at drastically reduced hardware costs. In receive AS, the receiver connects a dynamically selected subset of N available antennas to the L available RF chains. The "best" subset to be used for data reception is determined by means of channel estimates acquired using training sequences. Due to the nature of AS, the channel estimates at different antennas are obtained from different transmissions of the pilot sequence, and are, thus, outdated by different amounts in a time-varying channel. We show that a linear weighting of the estimates is optimum for the subset selection process, where the weights are related to the temporal correlation of the channel variations. When L is not an integer divisor of N, we highlight a new issue of "training voids", in which the last pilot transmission is not fully exploited by the receiver. We present a "void-filling" method for fully exploiting these voids, which essentially provides more accurate training for some antennas, and derive the optimal subset selection rule for any void-filling method. We also derive new closed-form equations for the performance of receive AS with optimal subset selection.

Relay selection combined with buffering of packets of relays can substantially increase the throughput of a cooperative network that uses rateless codes. However, buffering also increases the end-to-end delays due to the additional queuing delays at the relay nodes. In this paper we propose a novel method that exploits a unique property of rateless codes that enables a receiver to decode a packet from non-contiguous and unordered portions of the received signal. In it, each relay, depending on its queue length, ignores its received coded bits with a given probability. We show that this substantially reduces the end-to-end delays while retaining almost all of the throughput gain achieved by buffering. In effect, the method increases the odds that the packet is first decoded by a relay with a smaller queue. Thus, the queuing load is balanced across the relays and traded off with transmission times. We derive explicit necessary and sufficient conditions for the stability of this system when the various channels undergo fading. Despite encountering analytically intractable G/GI/1 queues in our system, we also gain insights about the method by analyzing a similar system with a simpler model for the relay-to-destination transmission times.

Receive antenna selection (AS), in which only a subset of antennas receive simultaneously at any time, requires the transmitter to send pilots multiple times so that the receiver can acquire channel state of all antennas and select the best subset. In conventional AS training, sensitivity of coherent reception to channel estimation errors forces the transmitter to boost the energy allocated to all pilots to ensure accurate channel estimates. Energy for pilots received by unselected antennas is mostly wasted, especially since the selection process is robust to estimation errors. In this paper, we propose a novel training method uniquely tailored for AS. Using one extra pilot symbol, accurate channel estimates get generated for the antenna subset that actually receives data. Consequently, the transmitter can selectively boost the energy allocated to the extra pilot. Other pilots, which now primarily help in subset selection, get allocated less energy. We derive closed-form expressions for the proposed scheme's symbol error probability, and optimize the energy allocated to pilot and data symbols. We show that the optimal solution achieves full diversity; it is provably unique and strictly better than the conventional model.

The use of energy harvesting (EH) nodes as cooperative relays is an attractive solution that harnesses the spatial diversity of a multi-relay network and also addresses the vexing problem of a relay's batteries getting drained when it forwards information to the destination. For a general class of stationary and ergodic energy harvesting processes, we analytically characterize the performance of a cooperative system in which the EH nodes are amplify-and-forward relays, which volunteer to relay if and only if they have sufficient energy for transmission. We show that when such systems employ relay selection, the energy usage at any relay and, consequently, its availability for relaying depend not only on its energy harvesting process but also the total number of relays and the relay selection policy. Further insight is gained by a two-fold asymptotic analysis that considers the cases where the signal-to-noise ratio (SNR) or the number of relays is large. The optimal static transmit power setting at the EH relays is also determined. Altogether, our results show that EH relays are beneficial and different from conventional cooperative relays.

Timer-based mechanisms are often used in several wireless systems to help a given (sink) node select the best helper node among many available nodes. Specifically, a node transmits a packet when its timer expires, and the timer value is a function of its local suitability metric. In practice, the best node gets selected successfully only if no other node's timer expires within a `vulnerability' window after its timer expiry. In this paper, we provide a complete closed-form characterization of the optimal metric-to-timer mapping that maximizes the probability of success for any probability distribution function of the metric. The optimal scheme is scalable, distributed, and much better than the popular inverse metric timer mapping. We also develop an asymptotic characterization of the optimal scheme that is elegant and insightful, and accurate even for a small number of nodes.

Hardware constraints, which motivate receive antenna selection, also require that various antenna elements at the receiver be sounded sequentially to obtain estimates required for selecting the 'best' antenna and for coherently demodulating data thereafter. Consequently, the channel state information at different antennas is outdated by different amounts and corrupted by noise. We show that, for this reason, simply selecting the antenna with the highest estimated channel gain is not optimum. Rather, a preferable strategy is to linearly weight the channel estimates of different antennas differently, depending on the training scheme. We derive closed-form expressions for the symbol error probability (SEP) of AS for MPSK and MQAM in time-varying Rayleigh fading channels for arbitrary selection weights, and validate them with simulations. We then characterize explicitly the optimal selection weights that minimize the SEP. We also consider packet reception, in which multiple symbols of a packet are received by the same antenna. New suboptimal, but computationally efficient weighted selection schemes are proposed for reducing the packet error rate. The benefits of weighted selection are also demonstrated using a practical channel code used in third generation cellular systems. Our results show that optimal weighted selection yields a significant performance gain over conventional unweighted selection.

Timer-based mechanisms are often used to help a given (sink) node select the best helper node from among many available nodes. In these, a node transmits a packet when its timer expires. The timer value is a monotone non-increasing function of its local suitability metric, which ensures that the best node is the first to transmit and is selected successfully if no other node's timer expires within a 'vulnerability' window after its timer expiry and so long as the sink can hear the available nodes. In this paper, we show that the optimal metric-to-timer mapping that (i) maximizes the probability of successful selection or (ii) minimizes the average selection time subject to a minimum constraint on the probability of success, maps the metric into a set of discrete timer values. We specify, in closed-form, the optimal scheme as a function of the maximum selection duration, the vulnerability window, and the number of nodes. An asymptotic characterization of the optimal scheme turns out to be elegant and insightful. For any probability distribution function of the metric, the optimal scheme is scalable, distributed, and performs much better than the popular inverse metric timer mapping. It even compares favorably with splitting-based selection, when the latter's feedback overhead is accounted for.

In receive antenna selection (AS), only signals from a subset of the antennas are processed at any time by the limited number of radio frequency (RF) chains available at the receiver. Hence, the transmitter needs to send pilots multiple times to enable the receiver to estimate the channel state of all the antennas and select the best subset. Conventionally, the sensitivity of coherent reception to channel estimation errors has been tackled by boosting the energy allocated to all pilots to ensure accurate channel estimates for all antennas. Energy for pilots received by unselected antennas is mostly wasted, especially since the selection process is robust to estimation errors. In this paper, we propose a novel training method uniquely tailored for AS that transmits one extra pilot symbol that generates accurate channel estimates for the antenna subset that actually receives data. Consequently, the transmitter can selectively boost the energy allocated to the extra pilot. We derive closed-form expressions for the proposed scheme's symbol error probability for MPSK and MQAM, and optimize the energy allocated to pilot and data symbols. Through an insightful asymptotic analysis, we show that the optimal solution achieves full diversity and is better than the conventional method.

The use of energy harvesting (EH) nodes as cooperative relays is a promising and emerging solution in wireless systems such as wireless sensor networks. It harnesses the spatial diversity of a multi-relay network and addresses the vexing problem of a relay's batteries getting drained in forwarding information to the destination. We consider a cooperative system in which EH nodes volunteer to serve as amplify-and-forward relays whenever they have sufficient energy for transmission. For a general class of stationary and ergodic EH processes, we introduce the notion of energy constrained and energy unconstrained relays and analytically characterize the symbol error rate of the system. Further insight is gained by an asymptotic analysis that considers the cases where the signal-to-noise-ratio or the number of relays is large. Our analysis quantifies how the energy usage at an EH relay and, consequently, its availability for relaying, depends not only on the relay's energy harvesting process, but also on its transmit power setting and the other relays in the system. The optimal static transmit power setting at the EH relays is also determined. Altogether, our results demonstrate how a system that uses EH relays differs in significant ways from one that uses conventional cooperative relays.

Relay selection for cooperative communications promises significant performance improvements, and is, therefore, attracting considerable attention. While several criteria have been proposed for selecting one or more relays, distributed mechanisms that perform the selection have received relatively less attention. In this paper, we develop a novel, yet simple, asymptotic analysis of a splitting-based multiple access selection algorithm to find the single best relay. The analysis leads to simpler and alternate expressions for the average number of slots required to find the best user. By introducing a new `contention load¿ parameter, the analysis shows that the parameter settings used in the existing literature can be improved upon. New and simple bounds are also derived. Furthermore, we propose a new algorithm that addresses the general problem of selecting the best Q ¿ 1 relays, and analyze and optimize it. Even for a large number of relays, the scalable algorithm selects the best two relays within 4.406 slots and the best three within 6.491 slots, on average. We also propose a new and simple scheme for the practically relevant case of discrete metrics. Altogether, our results develop a unifying perspective about the general problem of distributed selection in cooperative systems and several other multi-node systems.

A common and practical paradigm in cooperative communication systems is the use of a dynamically selected "best" relay to decode and forward information from a source to a destination. Such systems use two phases - a relay selection phase, in which the system uses transmission time and energy to select the best relay, and a data transmission phase, in which it uses the spatial diversity benefits of selection to transmit data. In this paper, we derive closed-form expressions for the overall throughput and energy consumption, and study the time and energy trade-off between the selection and data transmission phases. To this end, we analyze a baseline non-adaptive system and several adaptive systems that adapt the selection phase, relay transmission power, or transmission time. Our results show that while selection yields significant benefits, the selection phase's time and energy overhead can be significant. In fact, at the optimal point, the selection can be far from perfect, and depends on the number of relays and the mode of adaptation. The results also provide guidelines about the optimal system operating point for different modes of adaptation. The analysis also sheds new insights on the fast splitting-based algorithm considered in this paper for relay selection.

We develop an alternate characterization of the statistical distribution of the inter-cell interference power observed in the uplink of CDMA systems. We show that the lognormal distribution better matches the cumulative distribution and complementary cumulative distribution functions of the uplink interference than the conventionally assumed Gaussian distribution and variants based on it. This is in spite of the fact that many users together contribute to uplink interference, with the number of users and their locations both being random. Our observations hold even in the presence of power control and cell selection, which have hitherto been used to justify the Gaussian distribution approximation. The parameters of the lognormal are obtained by matching moments, for which detailed analytical expressions that incorporate wireless propagation, cellular layout, power control, and cell selection parameters are developed. The moment-matched lognormal model, while not perfect, is an order of magnitude better in modeling the interference power distribution.

Energy harvesting sensors (EHS), which harvest energy from the environment in order to sense and then communicate their measurements over a wireless link, provide the tantalizing possibility of perpetual lifetime operation of a sensor network. The wireless communication link design problem needs to be revisited for these sensors as the energy harvested can be random and small and not available when required. In this paper, we develop a simple model that captures the interactions between important parameters that govern the communication link performance of a EHS node, and analyze its outage probability for both slow fading and fast fading wireless channels. Our analysis brings out the critical importance of the energy profile and the energy storage capability on the EHS link performance. Our results show that properly tuning the transmission parameters of the EHS node and having even a small amount of energy storage capability improves the EHS link performance considerably.

A detailed characterization of interference power statistics in CDMA systems is of considerable practical and theoretical interest. Such a characterization for uplink inter-cell interference has been difficult because of transmit power control, randomness in the number of interfering mobile stations, and randomness in their locations. We develop a new method to model the uplink inter-cell interference power as a lognormal distribution, and show that it is an order of magnitude more accurate than the conventional Gaussian approximation even when the average number of mobile stations per cell is relatively large and even outperforms the moment-matched lognormal approximation considered in the literature. The proposed method determines the lognormal parameters by matching its moment generating function with a new approximation of the moment generating function for the inter-cell interference. The method is tractable and exploits the elegant spatial Poisson process theory. Using several numerical examples, the accuracy of the proposed method in modeling the probability distribution of inter-cell interference is verified for both small and large values of interference.

A common and practical paradigm in cooperative communications is the use of a dynamically selected 'best' relay to decode and forward information from a source to a destination. Such a system consists of two core phases: a relay selection phase, in which the system expends resources to select the best relay, and a data transmission phase, in which it uses the selected relay to forward data to the destination. In this paper, we study and optimize the trade-off between the selection and data transmission phase durations. We derive closed-form expressions for the overall throughput of a non-adaptive system that includes the selection phase overhead, and then optimize the selection and data transmission phase durations. Corresponding results are also derived for an adaptive system in which the relays can vary their transmission rates. Our results show that the optimal selection phase overhead can be significant even for fast selection algorithms. Furthermore, the optimal selection phase duration depends on the number of relays and whether adaptation is used.

Receive antenna selection (AS) reduces the hardware complexity of multi-antenna receivers by dynamically connecting an instantaneously best antenna element to the available radio frequency (RF) chain. Due to the hardware constraints, the channels at various antenna elements have to be sounded sequentially to obtain estimates that are required for selecting the "best" antenna and for coherently demodulating data. Consequently, the channel state information at different antennas is outdated by different amounts. We show that, for this reason, simply selecting the antenna with the highest estimated channel gain is not optimum. Rather, the channel estimates of different antennas should be weighted differently, depending on the training scheme. We derive closed-form expressions for the symbol error probability (SEP) of AS for MPSK and MQAM in time-varying Rayleigh fading channels for arbitrary selection weights, and validate them with simulations. We then derive an explicit formula for the optimal selection weights that minimize the SEP. We find that when selection weights are not used, the SEP need not improve as the number of antenna elements increases, which is in contrast to the ideal channel estimation case. However, the optimal selection weights remedy this situation and significantly improve performance.

Relay selection for cooperative communications has attracted considerable research interest recently. While several criteria have been proposed for selecting one or more relays and analyzed, mechanisms that perform the selection in a distributed manner have received relatively less attention. In this paper, we analyze a splitting algorithm for selecting the single best relay amongst a known number of active nodes in a cooperative network. We develop new and exact asymptotic analysis for computing the average number of slots required to resolve the best relay. We then propose and analyze a new algorithm that addresses the general problem of selecting the best Q ges 1 relays. Regardless of the number of relays, the algorithm selects the best two relays within 4.406 slots and the best three within 6.491 slots, on average. Our analysis also brings out an intimate relationship between multiple access selection and multiple access control algorithms.

Many wireless applications demand a fast mechanism to detect the packet from a node with the highest priority (ldquobest noderdquo) only, while packets from nodes with lower priority are irrelevant. In this paper, we introduce an extremely fast contention-based multiple access algorithm that selects the best node and requires only local information of the priorities of the nodes. The algorithm, which we call variable power multiple access selection (VP-MAS), uses the local channel state information from the accessing nodes to the receiver, and maps the priorities onto the receive power. It is based on a key result that shows that mapping onto a set of discrete receive power levels is optimal, when the power levels are chosen to exploit packet capture that inherently occurs in a wireless physical layer. The VP-MAS algorithm adjusts the expected number of users that contend in each step and their respective transmission powers, depending on whether previous transmission attempts resulted in capture, idle channel, or collision. We also show how reliable information regarding the total received power at the receiver can be used to improve the algorithm by enhancing the feedback mechanism. The algorithm detects the packet from the best node in 1.5 to 2.1 slots, which is considerably lower than the 2.43 slot average achieved by the best algorithm known to date.

Contention-based multiple access is a crucial component of many wireless systems. Multiple-packet reception (MPR) schemes that use interference cancellation techniques to receive and decode multiple packets that arrive simultaneously are known to be very efficient. However, the MPR schemes proposed in the literature require complex receivers capable of performing advanced signal processing over significant amounts of soft undecodable information received over multiple contention steps. In this paper, we show that local channel knowledge and elementary received signal strength measurements, which are available to many receivers today, can actively facilitate multi-packet reception and even simplify the interference canceling receiver's design. We introduce two variants of a simple algorithm called dual power multiple access (DPMA) that use local channel knowledge to limit the receive power levels to two values that facilitate successive interference cancellation. The resulting receiver structure is markedly simpler, as it needs to process only the immediate received signal without having to store and process signals received previously. Remarkably, using a set of three feedback messages, the first variant, DPMA-Lite, achieves a stable throughput of 0.6865 packets per slot. Using four possible feedback messages, the second variant, turbo-DPMA, achieves a stable throughput of 0.793 packets per slot, which is better than all contention algorithms known to date.

Cooperative communication using rateless codes, in which the source transmits an infinite number of parity bits to the destination until the receipt of an acknowledgment, has recently attracted considerable interest. It provides a natural and efficient mechanism for accumulating mutual information from multiple transmitting relays. We develop an analysis of queued cooperative relay systems that combines the communication-theoretic transmission aspects of cooperative communication using rateless codes over Rayleigh fading channels with the queuing-theoretic aspects associated with buffering messages at the relays. Relay cooperation combined with queuing reduces the message transmission times and also helps distribute the traffic load in the network, which improves throughput significantly.

The IEEE 802.16/WiMAX standard has fully embraced multi-antenna technology and can, thus, deliver robust and high transmission rates and higher system capacity. Nevertheless, due to its inherent form-factor constraints and cost concerns, a WiMAX mobile station (MS) should preferably contain fewer radio frequency (RF) chains than antenna elements. This is because RF chains are often substantially more expensive than antenna elements. Thus, antenna selection, wherein a subset of antennas is dynamically selected to connect to the limited RF chains for transceiving, is a highly appealing performance enhancement technique for multi-antenna WiMAX terminals. In this paper, a novel antenna selection protocol tailored for next-generation IEEE 802.16 mobile stations is proposed. As demonstrated by the extensive OPNET simulations, the proposed protocol delivers a significant performance improvement over conventional 802.16 terminals that lack the antenna selection capability. Moreover, the new protocol leverages the existing signaling methods defined in 802.16, thereby incurring a negligible signaling overhead and requiring only diminutive modifications of the standard. To the best of our knowledge, this paper represents the first effort to support antenna selection capability in IEEE 802.16 mobile stations.

In many wireless applications, it is highly desirable to have a fast mechanism to resolve or select the packet from the user with the highest priority. Furthermore, individual priorities are often known only locally at the users. In this paper we introduce an extremely fast, local-information-based multiple access algorithm that selects the best node in 1.8 to 2.1 slots, which is much lower than the 2.43 slot average achieved by the best algorithm known to date. The algorithm, which we call Variable Power Multiple Access Selection (VP-MAS), uses the local channel state information from the accessing nodes to the receiver, and maps the priorities into the receive power. It is inherently distributed and scales well with the number of users. We show that mapping onto a discrete set of receive power levels is optimal, and provide a complete characterization for it. The power levels are chosen to exploit packet capture that inherently occurs in a wireless physical layer. The VP-MAS algorithm adjusts the expected number of users that contend in each step and their respective transmission powers, depending on whether previous transmission attempts resulted in capture, idle channel, or collision.

Contention-based multiple access is a crucial component of many wireless systems. It is known that using interference cancellation techniques to receive and decode multiple packets that arrive simultaneously can improve the efficiency of multiple access. However, such multi-packet reception (MPR) schemes proposed in the literature require complex receivers capable of performing advanced signal processing over significant amounts of soft undecodable information received over multiple contention steps. In this paper, we show that local channel knowledge and elementary received signal strength measurements, which are made by many receivers today, can actively facilitate multi-packet reception and even simplify the interference canceling receiver's design. We introduce a simple algorithm called turbo-dual power multiple access (turbo-DPMA) that uses local channel knowledge to limit the receive power levels to two discrete values that are carefully chosen to facilitate successive interference cancellation. As we shall see, limiting the receive power in such a manner not only facilitates the simultaneous reception of up to two packets, but it also enables the receiver to derive additional useful information about the contending users from its received signal strength indicator. The resulting receiver structure is markedly simpler, as it needs to process only the immediate received signal, without having to store and process signals received previously. Even more remarkably, the turbo-DPMA is stable for packet arrival rates as high as 0.793 packets/slot, which is significantly better than all the contention algorithms known to date.

Wireless relays extend coverage, improve spectral efficiency, and enhance reliability and rates of wireless cellular communication systems. In this work, we introduce the fundamental notion of asymmetric cooperation among cooperating relays in cellular downlinks - different relays are party to different but overlapping knowledge about the messages transmitted from the base station. We argue that asymmetric cooperation arises naturally in most two-phase protocols in which the base station first transmits information to multiple relays that then cooperatively forward the information to the recipient mobile stations in the cell. For a system in which two relays are of the decode-and-forward type and cooperate using linear precoding to communicate with two mobile stations, we formulate the general, but complicated, throughput optimization problem and derive several results that considerably simplify the optimization. We show that under different channel configurations and fairness criteria, asymmetric cooperation is often the throughput-maximizing option. Under typical configurations, a 20-30% throughput enhancement is achieved compared to conventional full-cooperation systems.

We consider a cooperative wireless network where a set of nodes cooperate to relay in parallel the information from a source to a destination using a decode-and-forward approach. The source broadcasts the data to the relays, some or all of which cooperatively beamform to forward the data to the destination. We generalize the standard approaches for cooperative communications in two key respects: (i) we explicitly model and factor in the cost of acquiring channel state information (CSI), and (ii) we consider more general selection rules for the relays and compute the optimal one among them. In particular, we consider simple relay selection and outage criteria that exploit the inherent diversity of relay networks and satisfy a mandated outage constraint. These criteria include as special cases several relay selection criteria proposed in the literature. We obtain expressions for the total energy consumption for general relay selection and outage criteria for the non-homogeneous case, in which different relay links have different mean channel power gains, and the homogeneous case, in which the relay links statistics are identical. We characterize the structure of the optimal transmission scheme. Numerical results show that the cost of training and feedback of CSI is significant. The optimal strategy is to use a varying subset (and number) of relay nodes to cooperatively beamform at any given time. Depending on the relative location of the relays, the source, and the destination, numerical computations show energy savings of about 16% when an optimal relay selection rule is used. We also study the impact of shadowing correlation on the energy consumption for a cooperative relay network.

This paper considers a multi-hop network in which relay nodes cooperate to minimize the total energy consumed in transmitting a (unicast) packet from a source to a destination. We propose the Progressive Accumulative Routing (PAR) algorithm, which progressively performs relay discovery, relay ordering and relay power allocation in a distributed manner, such that each relay node only needs local information. We assume Destination Energy Accumulation, in which the destination accumulates the energy of multiple received copies of a packet, each of which is too weak to be reliably decoded by itself, while the lower complexity relay nodes use a decode-and-forward approach. We also provide a closed-form analysis of the energy-savings achieved by the PAR when a relay node is added to an already existing DEA route. Simulations verify that the algorithm considerably reduces the total energy consumption, and can be implemented efficiently.

Cooperative transmission by base stations (BSs) can significantly improve the spectral efficiency of multiuser, multicell, multiple input multiple output (MIMO) systems. We show that contrary to what is often assumed in the literature, the multiuser interference in such systems is fundamentally asynchronous. Intuitively, perfect timing-advance mechanisms can be best only ensure that the desired signal components- but not also the interference components- are perfectly aligned at their intended mobile stations. We develop an accurate mathematical model for the asynchronicity, and show that it leads to a significant performance degradation of existing designs that ignore the asynchronicity of interference. Using three previously proposed linear precoding design methods for BS cooperation, we develop corresponding algorithms that are better at mitigating the impact of the asynchronicity of the interference. Furthermore, we also address timing-advance inaccuracies (jitter), which are inevitable in a practical system. We show that using jitter-statistics-aware precoders can mitigate the impact of these inaccuracies as well. The insights are critical for the practical implementation of BS cooperation in multiuser MIMO systems, a topic that is typically oversimplified in the literature.

Fixed and mobile relays are used, among other applications, in the downlink of cellular communications systems. Cooperation between relays can greatly increase their benefits in terms of extended coverage, increased reliability, and improved spectral efficiency. In this paper, we introduce the fundamental notion of asymmetric cooperation. For this, we consider a two-phase transmission protocol where, in the first phase, the base station (BS) sends several available messages to the relays over wireless links. But, depending on the channel state and the duration of the BS transmission, not all relays decode all messages. In a second phase, the relays, which may now have asymmetric message knowledge, use cooperative linear precoding for the transmission to the mobile stations. We show that for many channel configurations, asymmetric cooperation, although (slighlty) sub-optimum for the second phase, is optimum from a total-throughput point of view, as it requires less time and energy in the first phase. We give analytical formulations for the optimum operating parameters and the achievable throughput, and show that under typical circumstances, 20-30% throughput enhancement can be achieved over conventional systems.

Accurate system planning and performance evaluation requires knowledge of the joint impact of scheduling, interference, and fading. However, current analyses either require costly numerical simulations or make simplifying assumptions that limit the applicability of the results. In this paper, we derive analytical expressions for the spectral efficiency of cellular systems that use either the channel-unaware but fair round robin scheduler or the greedy, channel-aware but unfair maximum signal to interference ratio scheduler. As is the case in real deployments, non-identical co-channel interference at each user, both Rayleigh fading and lognormal shadowing, and limited modulation constellation sizes are accounted for in the analysis. We show that using a simple moment generating function-based lognormal approximation technique and an accurate Gaussian-Q function approximation leads to results that match simulations well. These results are more accurate than erstwhile results that instead used the moment-matching Fenton-Wilkinson approximation method and bounds on the Q function. The spectral efficiency of cellular systems is strongly influenced by the channel scheduler and the small constellation size that is typically used in third generation cellular systems.

Cooperative transmission by base stations can significantly improve the spectral efficiency of multiuser, multi-cell multiple input multiple output systems. We show that in such systems the multiuser interference is asynchronous by nature, even when perfect timing-advance mechanisms ensure that the desired signal components arrive synchronously. We establish an accurate mathematical model for the asynchronism, and use it to show that the asynchronism leads to a significant performance degradation of existing linear preceding designs that assumed synchronous interference. We consider three different previously proposed precoding designs, and show how to modify them to effectively mitigate asynchronous interference.

In marked contrast with the ideal error-free feedback assumption that is common in the literature, practical systems are likely to have severely bandwidth-limited, error-prone feedback channels. We consider the scenario where feedback from the receiver is used by the transmitter to select the best antenna, out of many available antennas, for data transmission. Feedback errors cause the transmitter to select an antenna different from the one signaled by the receiver. We show that optimizing the signaling assignment, which maps the antenna indices to the feedback codewords, improves performance without introducing any additional redundancy. For a system that uses error-prone feedback to transmit quadrature-phase-shift-keying-modulated data from a single antenna selected from many available spatially correlated antennas, we derive closed-form approximations for the data symbol error probability for an arbitrary number of receive antennas. We use these to systematically find the optimal signaling assignments using a low-complexity algorithm. The optimal signaling is intimately coupled to how the receiver performs selection verification, i.e., how it decodes the data signal when, due to feedback errors, it does not always know which antenna was used for data transmission. We show that ignoring feedback errors at the receiver can lead to an unacceptable performance degradation, and develop optimal and suboptimal, blind and nonblind selection-verification methods. With a small side-information overhead, nonblind verification approaches the ideal perfect selection-verification performance

A simple, novel, and general method is presented in this paper for approximating the sum of independent or arbitrarily correlated lognormal random variables (RV) by a single lognormal RV. The method is also shown to be applicable for approximating the sum of lognormal-Rice and Suzuki RVs by a single lognormal RV. A sum consisting of a mixture of the above distributions can also be easily handled. The method uses the moment generating function (MGF) as a tool in the approximation and does so without the extremely precise numerical computations at a large number of points that were required by the previously proposed methods in the literature. Unlike popular approximation methods such as the Fenton-Wilkinson method and the Schwartz-Yeh method, which have their own respective short-comings, the proposed method provides the parametric flexibility to accurately approximate different portions of the lognormal sum distribution. The accuracy of the method is measured both visually, as has been done in the literature, as well as quantitatively, using curve-fitting metrics. An upper bound on the sensitivity of the method is also provided.

Cooperative communications, where parallel relays forward information to a destination node, can greatly improve the energy efficiency and latency in ad-hoc networks. However, current networks do not fully exploit its potential as they only use traditional energy-accumulation, which is often used in conjunction with repetition coding or cooperative space-time codes. In this paper, we show that the concept of mutual- information-accumulation can be realized with the help of fountain codes, and leads to a lower energy expenditure and a lower transmission time than energy accumulation. We then provide an analysis of the performance of mutual information accumulation in relay networks with N relay nodes. We first analyze the quasi-synchronuous scenario where the source stops transmitting and the relay nodes start transmitting after L relay nodes have successfully decoded the source data. We show that an optimum L exists, and is typically on the order of 3 or 4. We also give closed-form equations for the energy savings that can be achieved by the use of mutual-information-accumulation at the receiver. We then analyze and provide bounds for an alternate scenario where each relay node starts its transmission to the destination as soon as it has decoded the source data, independent of the state of the other relay nodes. This approach further reduces the transmission time, because the transmission by the relay nodes helps the other relay nodes that are still receiving.

We consider a MIMO system where error-prone feedback from the receiver is used by the transmitter to select a single optimum antenna to transmit data. Such error-prone feedback is common in the bandwidth-limited real systems, and is in marked contrast with the idealizations assumed in the selection literature. We show how the signaling assignment, which maps the antenna indices to the codewords that are fed back to indicate the index of the best transmit antenna, affects the performance of transmit antenna selection. The impact is intimately coupled with the receiver design. We derive approximate closed-form expressions for the average symbol error probability of QPSK modulated data in a spatially correlated channel, and then systematically find the optimal signaling assignment. Performance improvements are demonstrated for different antenna topologies without introducing any additional redundancy.

We consider a cooperative wireless network where the source broadcasts data to relays, some or all of which cooperatively beamform to forward the data to the destination. The network is subject to an overall outage constraint. We generalize the standard approaches for cooperative communications in two respects: (i) we explicitly model and factor in the cost of acquiring channel state information (CSI), and (ii) we consider more general, yet simple, selection rules for the relays and compute the optimal one among them. These rules include as special cases several relay selection criteria proposed in the literature. We present analytical results for the homogeneous case, where the links have identical mean channel gains. For this case, we show that the optimal transmission scheme is simple and can be computed efficiently. Numerical results show that while the cost of training and feedback of CSI is significant, relay cooperation is still beneficial.

We investigate a cooperative communications scheme withNparallel relays, where both the transmissions from the source to the relays and from the relays to the destination use fountain codes. Receivers for fountain codes can accumulate mutual information, while traditional energy collection methods, such as repetition or cooperative space-time codes, only accumulate energy. As a consequence, using fountain codes can reduce the total energy required for transmitting data from the source to the destination. We first analyze the scenario where the source stops transmitting and the relay nodes start transmitting afterLrelay nodes have successfully decoded the source data. We optimizeL, and also give closed-form equations for the energy savings that can be achieved by the use of mutual-information-collection at the receiver instead of traditional energy-collection methods. We then analyze an alternate scenario where each relay node starts its transmission to the destination as soon as it has decoded the source data, and helps the other relay nodes that are still in reception mode. Doing so further reduces the total transmission time and energy consumption.

This paper considers a sensor network where relay nodes cooperate in order to minimize the total energy consumption for the unicast transmission of a message from a single source to a single destination. We assume Destination Energy Accumulation, i.e., the destination can accumulate the energy of multiple copies of the message, each of which is too weak to be reliably decoded by itself, while the relay nodes use a decode-and-forward approach. We propose the Progressive Accumulative Routing (PAR) algorithm, which performs relay discovery, relay ordering and power allocation in a distributed manner so that each relay node only needs information about its neighboring nodes. Simulations verify that the algorithm considerably reduces the total energy consumption, and can be implemented efficiently. Furthermore, it performs close to the optimal DEA route with high probability.

A simple and novel method is presented to approximate by the lognormal distribution the probability density function of the sum of correlated lognormal random variables. The method is also shown to work well for approximating the distribution of the sum of lognormal-Rice or Suzuki random variables by the lognormal distribution. The method is based on matching a low-order Gauss-Hermite approximation of the moment-generating function of the sum of random variables with that of a lognormal distribution at a small number of points. Compared with methods available in the literature such as the Fenton-Wilkinson method, Schwartz-Yeh method, and their extensions, the proposed method provides the parametric flexibility to address the inevitable trade-off that needs to be made in approximating different regions of the probability distribution function.

The orthogonality factor (OF) quantifies the loss of orthogonality between the signals transmitted simultaneously on a wideband code division multiple access (WCDMA) downlink due to multipath dispersion. It is one of the fundamental parameters that determines the signal-to-interference-plus-noise ratio at the output of a Rake receiver and, consequently, it has a significant impact on downlink system capacity. The OF depends greatly on the delay profile of the multipath channel between the mobile and its serving base station; this profile varies considerably from one location in the cell to another. In this paper, we study how the statistical properties of the small-scale-fading-averaged OF vary over the entire macrocellular area. We use an ensemble of channel profiles at different locations in a cell generated from an implementation of the comprehensive COST259 channel model, which incorporates results from several experimental investigations. We show that the small-scale-fading-averaged OF is itself a random variable whose statistics depend on the mobile's distance from its serving base station. The large observed variance of the OF indicates that using a single value for all users in downlink capacity analyses and simulations, as has been the practice, may lead to erroneous conclusions. Finally, we propose a simple model that closely matches the statistics of the OF as a function of mobile-to-base distance, thus obviating the need to set up the complicated channel model every time OF values are to be generated

We introduce two novel joint radio-frequency (RF)-baseband designs for receivers in a MIMO system with Nttransmit antennas, Nrreceive antennas, but only LrRF chains at the receiver. The joint design introduces an RF pre-processing matrix that processes the signals from the different antennas, and is followed by selection (if necessary), down-conversion, and further processing in the baseband. The schemes are similar to conventional antenna selection in that they use fewer RF chains than antenna elements, but achieve superior performance by exploiting the spatial correlation of the received signals. The first of our proposed designs uses an L times NrRF pre-processing matrix that outputs only L streams followed by baseband signal processing, and, thus, eliminates the need for a selection switch. The second one uses an Nrtimes NrRF pre-processing matrix that outputs Nrstreams and is followed by a switch that selects L streams for baseband signal processing. Both spatial diversity and spatial multiplexing systems are considered and the optimum pre-processing matrices are derived for all cases. To accommodate practical RF design constraints, which prefer a variable phase-shifter-based implementation, a sub-optimal phase approximation is also introduced. Performance better than conventional antenna selection and close to the full complexity receiver is observed in both single cluster and multi-cluster wireless channels. A beam-pattern-based geometric intuition is also developed to illustrate the effectiveness of the optimal solutions

Multipath dispersion leads to the loss of orthogonality between signals transmitted simultaneously on a wide-band code division multiple access (WCDMA) downlink. The orthogonality factor (OF), which models its impact in the link signal-to-interference-plus-noise ratio (SINR) equation, depends - to a large extent - on the power delay profile of the multipath channel between the mobile and its serving base station. We use the comprehensive and general COST259 channel model for urban cellular environments to evaluate the impact on the OF of multipath clusters and distance-dependence of the multipath delay decay time constant, both of which have been observed in several channel measurements. The observed large standard deviation of the OF indicates that using a single value for all users in downlink capacity analyses and simulations, as has been the practice, may lead to erroneous conclusions. We also propose an empirical model to analytically characterize the observed statistics of the OF

We derive exact closed-form expressions for the system-level theoretical spectral efficiency of cellular radio systems that use channel-aware schedulers and operate in the presence of co-channel interference and noise. The co-channel interferers are not identically distributed, as is the case in typical cellular layouts. Accounting for non-identical interferers avoids the loose spectral efficiency bounds in the literature that only look at the worst case and best case locations of identical co-channel interferers. It also enables including the effect of second-tier interferers in the cellular layout, and leads to analytical results that are in excellent agreement with the simulation results. The spectral efficiencies of the greedy Max-SINR and the fair round-robin scheduler are compared. The detrimental effect of using small modulation alphabet sizes, as is the case in second and third generation cellular standards, is also quantified.

A simple and novel method is presented to approximate the distribution of the sum of independent, but not necessarily identical, lognormal random variables, by the lognormal distribution. It is shown that matching a short Gauss-Hermite approximation of the moment generating function of the lognormal sum with that of the lognormal distribution leads to an accurate lognormal sum approximation. The advantage of the proposed method over the ones in the literature, such as the Fenton-Wilkinson method, Schwartz-Yeh method, and the recently proposed Beaulieu-Xie method, is that it provides the parametric flexibility to handle the inevitable trade-off that needs to be made in approximating different regions of the probability distribution function. The accuracy is verified using extensive simulations based on a cellular layout

For a multiple input multiple output system, antenna selection reduces complexity at the expense of performance. In this paper, we propose two novel RF pre-processing architectures that significantly improve the performance of antenna selection, while marginally increasing the complexity. These architectures introduce an RF pre-processing matrix, M, that multiplies the vector of incoming signals prior to downconversion. The elements of M use only the knowledge of the channel statistics. In the first architecture, M outputs a reduced number of streams - an explicit selection algorithm is therefore not required. In the second architecture, the number of output streams equals the number of input streams, and the reduction of the number of streams is achieved by a selection switch that uses instantaneous channel state information. We show that the optimal pre-processing receiver projects the received signal along the eigenvectors of the correlation matrix. In a correlated channel, both these architectures significantly outperform conventional antenna selection. We also develop a beam-pattern based intuition and compare the performance of our scheme to other RF preprocessing schemes previously proposed in the literature.

The loss of orthogonality between the spreading codes in a wideband code-division multiple-access downlink is modeled in analysis and simulations by means of the orthogonality factor (OF). The OF, which is an important parameter limiting downlink capacity, increases with the multipath dispersion in the channel. We utilize this relationship between the OF and the channel dispersion to show a novel, simple, and accurate way to determine the time-averaged OF directly from the channel delay profile. To this end, we define the diversity factor (DF) of a channel profile, derive the expression for it, and show that the DF and the OF are related by a simple mathematical relationship. We then verify our approach over an entire ensemble of channel profiles generated by the general COST259 macrocellular channel model.

The presence of multipaths leads to a loss of orthogonality between signals transmitted simultaneously on a wideband code-division multiple access (WCDMA) downlink. We derive general analytical expressions for the orthogonality factor (OF), which quantifies this loss of orthogonality, as a function of the instantaneous multipath fade realization of the channel. We show that the OF exhibits a significant temporal variation for the three channel profiles suggested in the WCDMA standard, namely, typical urban and rural areas and hilly terrain, which span a wide range of realistic cases. Moreover, its temporal variations and statistics vary significantly from one channel profile to another. Also, while the pulse shape and the number of RAKE fingers has only a marginal impact on the OF's statistics, the granularity in setting the finger positions has a considerable impact. The results of the work can be directly used for evaluation of the system performance of WCDMA cellular systems.

We analyze the clustering of scatterers in mobile radio channels, i.e, the fact that scatterers are usually not located uniformly in the whole coverage area, but tend to occur in clusters. While this has been recognized for some time, a realistic model for this phenomenon has been lacking up to now. We first analyze measurements to extract the distribution of the number of observed clusters. We then present a model that reflects not only this distribution, but also reproduces the appearance and disappearance of clusters as the mobile station moves through the cell. Our approach has been adopted as an important part of the COST259 directional channel model, a standard model for directional mobile radio channels. Finally, we discuss the implications of the model for the system performance of CDMA and SDMA systems.

We study the data performance of WCDMA systems using the downlink shared channel (DSCH) by investigating the impact of loading, rate adaptation and power control for the typical urban (TU) channel. We conclude that, using DSCH, high speed data transmissions can be achieved if the offered traffic load is well controlled. We discuss a heuristic rate adaptation algorithm that adapts the transmission rate based upon the perceived user performance in previous frames. We show that the performance of the rate adaptation is significantly better than that for the fixed-rate allocation policy.

The presence of multipath leads to a loss of orthogonality between the signals transmitted simultaneously on a WCDMA downlink. We derive general analytical expressions for the orthogonality factor (OF), which quantifies this loss of orthogonality. We show that the orthogonality factor exhibits a significant temporal variation for the three channel profiles suggested in the WCDMA standard, namely, typical urban, rural area, and hilly terrain, which span a wide range of realistic cases. Moreover, its temporal variations and statistics vary significantly from one channel profile to another. Also, while the pulse shape and the number of RAKE fingers has only a marginal impact on the OF's statistics, the granularity in setting the finger positions has a considerable impact. The results of the work can be directly used for evaluation of the system performance of WCDMA cellular systems.

PRMA, a packetized multiple access scheme for transmitting over short range radio channels, is a promising scheme to implement in a cellular system. PRMA requires little central control and allows hand-overs with minimal base station intervention. However, when mobile voice terminals move from one cell to another, they forfeit the slots reserved for them and, in addition, encounter hand-off delays leading to dropping of voice packets. The main problem is that a mobile terminal can lose more packets even after having secured a reservation. In this paper we use a path enumeration technique using signal flow graphs combined with equilibrium point analysis to analyze the effect of terminal mobility on the performance of PRMA in a cellular environment.

We analyze the performance of a link adaptation scheme in which a user, based on his SIR estimate, either transmits using a given modulation and coding scheme or does not transmit (backs off). The impact of channel correlation on the optimal back off SIR threshold is studied for a co-channel interference limited cellular system. Expressions are derived for the average packet waiting time given the basic system parameters like packet arrival statistics, channel fade statistics, number of users per cell, and link adaptation thresholds. Analysis results are shown to be in good agreement with the simulation results. We show that the optimal back-off threshold crucially depends on the channel correlation, a fact not considered by the formulae suggested in literature for determining the link adaptation thresholds. For channel correlation /spl rho/=0.82, the back-off mechanism could reduce average packet delay by up to 15%, as compared to the no back-off case. No such improvement was found for /spl rho/=0.41.

For a voice user in PRMA, a packet header error leads to the loss of slot reservation while a packet data error only causes a rejection of the transmitted packet. We use equilibrium point analysis and a path enumeration technique for signal flow graphs to analyze the effect of voice packet header and data errors on the performance of PRMA. The technique provides an improvement over the solutions previously suggested in literature. We also extend the analysis to model the effect of cochannel inter-cellular interference and error correction coding on PRMA over fading channels. Analytically obtained results for fixed packet error rates and for packet error rates that depend on the co-channel inter-cellular interference in the system are presented. The limitations of the analytical technique are also discussed.

We use equilibrium point analysis to analyze the effect of terminal mobility on the performance of PRMA in a cellular environment. We derive expressions for PRMA's throughput and packet dropping probability, in the presence of terminal mobility. We employ a path enumeration technique based on Mason's (1960) gain formula for signal flow graphs to evaluate the packet dropping probability. We present results showing the marginal effect that terminal mobility has on PRMA's performance.